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| Unknown | 1996-07-11 | 14.9 KB |
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| Confidence | Program | Detection | Match Type | Support
|
|---|
| 1%
| dexvert
| Eclipse Tutorial (other/eclipseTutorial)
| ext
| Unsupported |
| 1%
| dexvert
| JuggleKrazy Tutorial (other/juggleKrazyTutorial)
| ext
| Unsupported |
| 100%
| file
| data
| default
| |
| 100%
| gt2
| Kopftext: 'TUTOR 06['
| default (weak)
|
|
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 54 55 54 4f 52 20 30 36 | 5b 3a 00 00 42 01 00 00 |TUTOR 06|[:..B...|
|00000010| 53 65 63 74 69 6f 6e 20 | 31 2e 36 20 20 4f 74 68 |Section |1.6 Oth|
|00000020| 65 72 20 54 79 70 65 73 | 20 6f 66 20 45 71 75 61 |er Types| of Equa|
|00000030| 74 69 6f 6e 73 0d 0a 00 | 0d 0b 00 0e 65 31 2d 36 |tions...|....e1-6|
|00000040| 2d 31 0e 47 75 69 64 65 | 64 20 45 78 61 6d 70 6c |-1.Guide|d Exampl|
|00000050| 65 20 20 31 0f 20 20 53 | 6f 6c 76 69 6e 67 20 61 |e 1. S|olving a|
|00000060| 20 50 6f 6c 79 6e 6f 6d | 69 61 6c 20 45 71 75 61 | Polynom|ial Equa|
|00000070| 74 69 6f 6e 20 62 79 20 | 46 61 63 74 6f 72 69 6e |tion by |Factorin|
|00000080| 67 0d 0a 00 0d 0b 00 0e | 65 31 2d 36 2d 32 0e 47 |g.......|e1-6-2.G|
|00000090| 75 69 64 65 64 20 45 78 | 61 6d 70 6c 65 20 20 32 |uided Ex|ample 2|
|000000a0| 0f 20 20 53 6f 6c 76 69 | 6e 67 20 61 20 50 6f 6c |. Solvi|ng a Pol|
|000000b0| 79 6e 6f 6d 69 61 6c 20 | 45 71 75 61 74 69 6f 6e |ynomial |Equation|
|000000c0| 20 62 79 20 46 61 63 74 | 6f 72 69 6e 67 0d 0a 00 | by Fact|oring...|
|000000d0| 0d 0b 00 0e 65 31 2d 36 | 2d 33 0e 47 75 69 64 65 |....e1-6|-3.Guide|
|000000e0| 64 20 45 78 61 6d 70 6c | 65 20 20 33 0f 20 20 53 |d Exampl|e 3. S|
|000000f0| 6f 6c 76 69 6e 67 20 61 | 6e 20 45 71 75 61 74 69 |olving a|n Equati|
|00000100| 6f 6e 20 6f 66 20 51 75 | 61 64 72 61 74 69 63 20 |on of Qu|adratic |
|00000110| 54 79 70 65 0d 0a 00 0d | 0b 00 0e 65 31 2d 36 2d |Type....|...e1-6-|
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|00000140| 20 45 71 75 61 74 69 6f | 6e 20 6f 66 20 51 75 61 | Equatio|n of Qua|
|00000150| 64 72 61 74 69 63 20 54 | 79 70 65 0d 0a 00 0d 0b |dratic T|ype.....|
|00000160| 00 0e 65 31 2d 36 2d 35 | 0e 47 75 69 64 65 64 20 |..e1-6-5|.Guided |
|00000170| 45 78 61 6d 70 6c 65 20 | 20 35 0f 20 20 53 6f 6c |Example | 5. Sol|
|00000180| 76 69 6e 67 20 61 6e 20 | 45 71 75 61 74 69 6f 6e |ving an |Equation|
|00000190| 20 48 61 76 69 6e 67 20 | 4f 6e 65 20 52 61 64 69 | Having |One Radi|
|000001a0| 63 61 6c 0d 0a 00 0d 0b | 00 0e 65 31 2d 36 2d 36 |cal.....|..e1-6-6|
|000001b0| 0e 47 75 69 64 65 64 20 | 45 78 61 6d 70 6c 65 20 |.Guided |Example |
|000001c0| 20 36 0f 20 20 41 6e 20 | 45 71 75 61 74 69 6f 6e | 6. An |Equation|
|000001d0| 20 49 6e 76 6f 6c 76 69 | 6e 67 20 61 20 52 61 74 | Involvi|ng a Rat|
|000001e0| 69 6f 6e 61 6c 20 45 78 | 70 6f 6e 65 6e 74 0d 0a |ional Ex|ponent..|
|000001f0| 00 0d 0b 00 0e 65 31 2d | 36 2d 37 0e 47 75 69 64 |.....e1-|6-7.Guid|
|00000200| 65 64 20 45 78 61 6d 70 | 6c 65 20 20 37 0f 20 20 |ed Examp|le 7. |
|00000210| 41 6e 20 45 71 75 61 74 | 69 6f 6e 20 49 6e 76 6f |An Equat|ion Invo|
|00000220| 6c 76 69 6e 67 20 46 72 | 61 63 74 69 6f 6e 73 0d |lving Fr|actions.|
|00000230| 0a 00 0d 0b 00 0e 65 31 | 2d 36 2d 38 0e 47 75 69 |......e1|-6-8.Gui|
|00000240| 64 65 64 20 45 78 61 6d | 70 6c 65 20 20 38 0f 20 |ded Exam|ple 8. |
|00000250| 20 41 6e 20 45 71 75 61 | 74 69 6f 6e 20 49 6e 76 | An Equa|tion Inv|
|00000260| 6f 6c 76 69 6e 67 20 41 | 62 73 6f 6c 75 74 65 20 |olving A|bsolute |
|00000270| 56 61 6c 75 65 0d 0a 00 | 0d 0b 00 0e 65 31 2d 36 |Value...|....e1-6|
|00000280| 2d 39 0e 47 75 69 64 65 | 64 20 45 78 61 6d 70 6c |-9.Guide|d Exampl|
|00000290| 65 20 20 39 0f 20 20 41 | 6e 20 41 70 70 6c 69 63 |e 9. A|n Applic|
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|000002b0| 72 20 61 20 50 72 6f 64 | 75 63 74 0d 0a 00 0d 0b |r a Prod|uct.....|
|000002c0| 00 0e 69 31 2d 36 2d 31 | 0e 49 6e 74 65 67 72 61 |..i1-6-1|.Integra|
|000002d0| 74 65 64 20 45 78 61 6d | 70 6c 65 20 20 31 0f 20 |ted Exam|ple 1. |
|000002e0| 20 41 20 52 61 64 69 63 | 61 6c 20 45 71 75 61 74 | A Radic|al Equat|
|000002f0| 69 6f 6e 20 74 68 61 74 | 20 43 6f 6e 76 65 72 74 |ion that| Convert|
|00000300| 73 20 74 6f 20 61 20 4e | 6f 6e 6c 69 6e 65 61 72 |s to a N|onlinear|
|00000310| 20 45 71 75 61 74 69 6f | 6e 0d 0a 00 0d 0b 00 0e | Equatio|n.......|
|00000320| 69 31 2d 36 2d 32 0e 49 | 6e 74 65 67 72 61 74 65 |i1-6-2.I|ntegrate|
|00000330| 64 20 45 78 61 6d 70 6c | 65 20 20 31 0f 20 20 52 |d Exampl|e 1. R|
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|00000350| 6e 67 20 42 6f 74 68 20 | 53 69 64 65 73 20 6f 66 |ng Both |Sides of|
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|00000370| 65 63 74 69 6f 6e 20 31 | 2e 36 20 20 4f 74 68 65 |ection 1|.6 Othe|
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|000003b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
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|00000430| 73 20 61 6c 72 65 61 64 | 79 20 69 6e 20 73 74 61 |s alread|y in sta|
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|00000460| 20 73 69 64 65 29 2c 0d | 0a 00 77 65 20 62 65 67 | side),.|..we beg|
|00000470| 69 6e 20 62 79 20 66 61 | 63 74 6f 72 69 6e 67 2e |in by fa|ctoring.|
|00000480| 13 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |.... | |
|00000490| 20 20 20 20 11 32 34 0d | 0b 00 20 20 20 20 20 20 | .24.|.. |
|000004a0| 20 20 20 20 20 20 20 20 | 20 11 33 78 20 20 11 31 | | .3x .1|
|000004b0| 2d 20 32 35 36 20 3d 20 | 30 20 20 20 20 20 20 20 |- 256 = |0 |
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|000004e0| 0a 00 20 20 20 20 20 20 | 20 11 32 32 20 20 20 20 |.. | .22 |
|000004f0| 20 20 20 20 32 0d 0b 00 | 20 20 20 20 20 11 31 28 | 2...| .1(|
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|00000510| 20 20 11 31 2d 20 31 36 | 29 20 3d 20 30 20 20 20 | .1- 16|) = 0 |
|00000520| 20 20 20 20 20 20 20 20 | 20 20 20 20 12 31 11 32 | | .1.2|
|00000530| 46 61 63 74 6f 72 20 61 | 73 20 74 68 65 20 64 69 |Factor a|s the di|
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|00000560| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000570| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000580| 20 20 20 20 20 20 20 11 | 31 12 31 20 20 20 20 20 | .|1.1 |
|00000590| 20 20 20 20 11 32 32 20 | 20 20 20 20 20 11 31 12 | .22 | .1.|
|000005a0| 30 0d 0b 00 28 11 33 78 | 20 20 11 31 2b 20 31 36 |0...(.3x| .1+ 16|
|000005b0| 29 28 11 33 78 20 11 31 | 2b 20 34 29 28 11 33 78 |)(.3x .1|+ 4)(.3x|
|000005c0| 20 11 31 2d 20 34 29 20 | 3d 20 30 20 20 20 20 20 | .1- 4) |= 0 |
|000005d0| 20 20 20 20 20 20 20 20 | 20 20 12 31 11 32 46 61 | | .1.2Fa|
|000005e0| 63 74 6f 72 20 28 78 20 | 20 2d 20 31 36 29 11 31 |ctor (x | - 16).1|
|000005f0| 12 30 13 0d 0a 00 0d 0a | 00 57 65 20 6e 6f 77 20 |.0......|.We now |
|00000600| 73 65 74 20 65 61 63 68 | 20 66 61 63 74 6f 72 20 |set each| factor |
|00000610| 65 71 75 61 6c 20 74 6f | 20 7a 65 72 6f 2e 13 0d |equal to| zero...|
|00000620| 0a 00 20 20 20 20 20 20 | 20 20 20 20 11 32 32 20 |.. | .22 |
|00000630| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000640| 32 0d 0b 00 20 20 20 20 | 20 20 20 20 20 11 33 78 |2... | .3x|
|00000650| 20 20 11 31 2b 20 31 36 | 20 3d 20 30 20 20 11 34 | .1+ 16| = 0 .4|
|00000660| 35 35 36 20 20 11 33 78 | 20 20 11 31 3d 20 2d 31 |556 .3x| .1= -1|
|00000670| 36 20 20 20 20 20 20 20 | 12 31 11 32 4e 6f 20 72 |6 |.1.2No r|
|00000680| 65 61 6c 20 73 6f 6c 75 | 74 69 6f 6e 11 31 12 30 |eal solu|tion.1.0|
|00000690| 13 0d 0a 00 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |....... | |
|000006a0| 20 20 11 33 78 20 11 31 | 2b 20 34 20 3d 20 30 20 | .3x .1|+ 4 = 0 |
|000006b0| 20 11 34 35 35 36 20 20 | 11 33 78 20 11 31 3d 20 | .4556 |.3x .1= |
|000006c0| 2d 34 13 0d 0a 00 0d 0b | 00 20 20 20 20 20 20 20 |-4......|. |
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|00000750| 20 69 6e 20 74 68 65 20 | 6f 72 69 67 69 6e 61 6c | in the |original|
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|00000780| 54 79 70 65 73 20 6f 66 | 20 45 71 75 61 74 69 6f |Types of| Equatio|
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|000007a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000007b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 | | .2|
|000007c0| 36 20 20 20 20 20 34 20 | 20 20 20 32 0d 0b 00 11 |6 4 | 2....|
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|000007e0| 6f 6c 75 74 69 6f 6e 73 | 20 6f 66 20 74 68 65 20 |olutions| of the |
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|00000810| 20 11 31 2d 20 39 20 3d | 20 30 2e 0d 0a 00 0d 0b | .1- 9 =| 0......|
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|00000850| 20 20 11 31 2d 20 39 11 | 33 78 20 20 11 31 2b 20 | .1- 9.|3x .1+ |
|00000860| 11 33 78 20 20 11 31 2d | 20 39 20 3d 20 30 20 20 |.3x .1-| 9 = 0 |
|00000870| 20 20 20 20 20 20 20 20 | 20 20 20 20 12 31 11 32 | | .1.2|
|00000880| 47 69 76 65 6e 20 65 71 | 75 61 74 69 6f 6e 11 31 |Given eq|uation.1|
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|000008a0| 20 34 20 20 20 20 20 20 | 32 0d 0b 00 20 11 31 28 | 4 |2... .1(|
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|000008c0| 29 20 2b 20 28 11 33 78 | 20 20 11 31 2d 20 39 29 |) + (.3x| .1- 9)|
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|00000900| 32 20 20 20 20 20 20 20 | 20 20 20 32 20 20 20 20 |2 | 2 |
|00000910| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000920| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00000930| 31 12 31 11 32 34 11 31 | 12 30 0d 0b 00 20 11 33 |1.1.24.1|.0... .3|
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|00000950| 20 2b 20 28 11 33 78 20 | 20 11 31 2d 20 39 29 20 | + (.3x | .1- 9) |
|00000960| 3d 20 30 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |= 0 | |
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|000009a0| 20 20 20 20 20 32 20 20 | 20 20 20 20 20 34 20 20 | 2 | 4 |
|000009b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000009c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000009d0| 20 20 11 31 12 31 11 32 | 32 11 31 12 30 0d 0b 00 | .1.1.2|2.1.0...|
|000009e0| 20 20 20 20 20 20 28 11 | 33 78 20 20 11 31 2d 20 | (.|3x .1- |
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|00000a30| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00000a40| 20 34 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | 4 | |
|00000a50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000a60| 20 20 11 31 12 31 11 32 | 32 11 31 12 30 0d 0b 00 | .1.1.2|2.1.0...|
|00000a70| 28 11 33 78 20 11 31 2b | 20 33 29 28 11 33 78 20 |(.3x .1+| 3)(.3x |
|00000a80| 11 31 2d 20 33 29 28 11 | 33 78 20 20 11 31 2b 20 |.1- 3)(.|3x .1+ |
|00000a90| 31 29 20 3d 20 30 20 20 | 20 20 20 20 20 20 20 20 |1) = 0 | |
|00000aa0| 20 20 20 20 12 31 11 32 | 46 61 63 74 6f 72 20 28 | .1.2|Factor (|
|00000ab0| 78 20 20 2d 20 39 29 11 | 31 12 30 11 32 13 0d 0a |x - 9).|1.0.2...|
|00000ac0| 00 0d 0a 00 11 31 57 65 | 20 6e 6f 77 20 73 65 74 |.....1We| now set|
|00000ad0| 20 65 61 63 68 20 66 61 | 63 74 6f 72 20 65 71 75 | each fa|ctor equ|
|00000ae0| 61 6c 20 74 6f 20 7a 65 | 72 6f 2e 13 0d 0a 00 0d |al to ze|ro......|
|00000af0| 0b 00 20 20 20 20 20 20 | 11 33 78 20 11 31 2b 20 |.. |.3x .1+ |
|00000b00| 33 20 3d 20 30 20 20 11 | 34 35 35 35 35 36 20 20 |3 = 0 .|455556 |
|00000b10| 20 11 33 78 20 11 31 3d | 20 2d 33 13 0d 0a 00 0d | .3x .1=| -3.....|
|00000b20| 0b 00 20 20 20 20 20 20 | 11 33 78 20 11 31 2d 20 |.. |.3x .1- |
|00000b30| 33 20 3d 20 30 20 20 11 | 34 35 35 35 35 36 20 20 |3 = 0 .|455556 |
|00000b40| 20 11 33 78 20 11 31 3d | 20 33 13 0d 0a 00 20 20 | .3x .1=| 3.... |
|00000b50| 20 20 20 20 11 32 34 20 | 20 20 20 20 20 20 20 20 | .24 | |
|00000b60| 20 20 20 20 20 20 20 20 | 20 34 0d 0b 00 20 20 20 | | 4... |
|00000b70| 20 20 11 33 78 20 20 11 | 31 2b 20 31 20 3d 20 30 | .3x .|1+ 1 = 0|
|00000b80| 20 20 11 34 35 35 35 35 | 36 20 20 11 33 78 20 20 | .45555|6 .3x |
|00000b90| 11 31 3d 20 2d 31 20 20 | 20 20 20 20 20 20 20 12 |.1= -1 | .|
|00000ba0| 31 11 32 4e 6f 20 72 65 | 61 6c 20 73 6f 6c 75 74 |1.2No re|al solut|
|00000bb0| 69 6f 6e 11 31 12 30 00 | 0c 0d 0a 00 54 68 75 73 |ion.1.0.|....Thus|
|00000bc0| 2c 20 74 68 65 20 65 71 | 75 61 74 69 6f 6e 20 68 |, the eq|uation h|
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|00000be0| 3a 20 2d 33 20 61 6e 64 | 20 33 2e 20 20 54 72 79 |: -3 and| 3. Try|
|00000bf0| 20 63 68 65 63 6b 69 6e | 67 20 65 61 63 68 20 6f | checkin|g each o|
|00000c00| 66 20 74 68 65 73 65 20 | 0d 0a 00 73 6f 6c 75 74 |f these |...solut|
|00000c10| 69 6f 6e 73 20 69 6e 20 | 74 68 65 20 6f 72 69 67 |ions in |the orig|
|00000c20| 69 6e 61 6c 20 65 71 75 | 61 74 69 6f 6e 2e 0d 0a |inal equ|ation...|
|00000c30| 00 53 65 63 74 69 6f 6e | 20 31 2e 36 20 20 4f 74 |.Section| 1.6 Ot|
|00000c40| 68 65 72 20 54 79 70 65 | 73 20 6f 66 20 45 71 75 |her Type|s of Equ|
|00000c50| 61 74 69 6f 6e 73 0d 0b | 00 20 20 20 20 20 20 20 |ations..|. |
|00000c60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000c70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000c80| 20 20 20 20 20 20 20 20 | 11 32 33 20 20 20 20 36 | |.23 6|
|00000c90| 0d 0b 00 11 31 46 69 6e | 64 20 74 68 65 20 72 65 |....1Fin|d the re|
|00000ca0| 61 6c 20 73 6f 6c 75 74 | 69 6f 6e 73 20 6f 66 20 |al solut|ions of |
|00000cb0| 74 68 65 20 65 71 75 61 | 74 69 6f 6e 20 31 35 20 |the equa|tion 15 |
|00000cc0| 2b 20 32 11 33 78 20 20 | 11 31 2d 20 11 33 78 20 |+ 2.3x |.1- .3x |
|00000cd0| 20 11 31 3d 20 30 2e 0d | 0a 00 0d 0b 00 13 12 31 | .1= 0..|.......1|
|00000ce0| 53 4f 4c 55 54 49 4f 4e | 12 30 0d 0a 00 20 20 20 |SOLUTION|.0... |
|00000cf0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000d00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000d10| 20 20 20 20 20 20 20 20 | 20 20 11 32 33 0d 0b 00 | | .23...|
|00000d20| 11 31 54 68 69 73 20 65 | 71 75 61 74 69 6f 6e 20 |.1This e|quation |
|00000d30| 69 73 20 6f 66 20 71 75 | 61 64 72 61 74 69 63 20 |is of qu|adratic |
|00000d40| 74 79 70 65 20 77 69 74 | 68 20 11 33 75 20 11 31 |type wit|h .3u .1|
|00000d50| 3d 20 11 33 78 20 11 31 | 2e 20 20 54 68 75 73 2c |= .3x .1|. Thus,|
|00000d60| 20 77 65 20 66 61 63 74 | 6f 72 20 74 68 65 20 6c | we fact|or the l|
|00000d70| 65 66 74 20 73 69 64 65 | 0d 0a 00 6f 66 20 74 68 |eft side|...of th|
|00000d80| 65 20 65 71 75 61 74 69 | 6f 6e 20 61 73 20 74 68 |e equati|on as th|
|00000d90| 65 20 70 72 6f 64 75 63 | 74 20 6f 66 20 74 77 6f |e produc|t of two|
|00000da0| 20 74 68 69 72 64 2d 64 | 65 67 72 65 65 20 70 6f | third-d|egree po|
|00000db0| 6c 79 6e 6f 6d 69 61 6c | 73 2e 13 0d 0a 00 0d 0b |lynomial|s.......|
|00000dc0| 00 20 20 20 20 20 20 20 | 20 20 20 11 32 33 20 20 |. | .23 |
|00000dd0| 20 20 36 0d 0b 00 20 20 | 20 11 31 31 35 20 2b 20 | 6... | .115 + |
|00000de0| 32 11 33 78 20 20 11 31 | 2d 20 11 33 78 20 20 11 |2.3x .1|- .3x .|
|00000df0| 31 3d 20 30 20 20 20 20 | 20 20 20 20 20 20 12 31 |1= 0 | .1|
|00000e00| 11 32 47 69 76 65 6e 20 | 65 71 75 61 74 69 6f 6e |.2Given |equation|
|00000e10| 11 31 12 30 11 32 13 0d | 0a 00 20 20 20 20 20 20 |.1.0.2..|.. |
|00000e20| 20 33 20 20 20 20 20 33 | 20 32 20 20 20 20 20 20 | 3 3| 2 |
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|00000e40| 20 20 20 11 31 12 31 11 | 32 32 20 20 20 20 20 20 | .1.1.|22 |
|00000e50| 20 20 20 20 20 33 11 31 | 12 30 0d 0b 00 31 35 20 | 3.1|.0...15 |
|00000e60| 2b 20 32 11 33 78 20 20 | 11 31 2d 20 28 11 33 78 |+ 2.3x |.1- (.3x|
|00000e70| 20 11 31 29 20 20 3d 20 | 30 20 20 20 20 20 20 20 | .1) = |0 |
|00000e80| 20 20 20 12 31 11 32 63 | 20 2b 20 62 75 20 2b 20 | .1.2c| + bu + |
|00000e90| 61 75 20 20 3d 20 30 2c | 20 75 20 3d 20 78 20 11 |au = 0,| u = x .|
|00000ea0| 31 12 30 11 32 13 0d 0a | 00 20 20 20 20 20 20 33 |1.0.2...|. 3|
|00000eb0| 20 20 20 20 20 20 20 33 | 0d 0b 00 11 31 28 35 20 | 3|....1(5 |
|00000ec0| 2d 20 11 33 78 20 11 31 | 29 28 33 20 2b 20 11 33 |- .3x .1|)(3 + .3|
|00000ed0| 78 20 11 31 29 20 3d 20 | 30 20 20 20 20 20 20 20 |x .1) = |0 |
|00000ee0| 20 20 20 12 31 11 32 46 | 61 63 74 6f 72 11 31 12 | .1.2F|actor.1.|
|00000ef0| 30 11 32 13 0d 0a 00 0d | 0a 00 11 31 57 65 20 6e |0.2.....|...1We n|
|00000f00| 6f 77 20 73 65 74 20 65 | 61 63 68 20 66 61 63 74 |ow set e|ach fact|
|00000f10| 6f 72 20 65 71 75 61 6c | 20 74 6f 20 7a 65 72 6f |or equal| to zero|
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|00000f80| 20 20 20 33 11 34 66 0d | 0b 00 20 20 20 11 31 35 | 3.4f.|.. .15|
|00000f90| 20 2d 20 11 33 78 20 20 | 11 31 3d 20 30 20 20 11 | - .3x |.1= 0 .|
|00000fa0| 34 35 35 35 35 36 20 20 | 11 31 35 20 3d 20 11 33 |455556 |.15 = .3|
|00000fb0| 78 20 20 20 20 11 34 35 | 35 35 35 36 20 20 11 33 |x .45|5556 .3|
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|00001000| 32 0d 0b 00 20 20 20 20 | 20 20 20 20 11 32 33 20 |2... | .23 |
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|00001030| 33 11 34 66 0d 0b 00 20 | 20 20 11 31 33 20 2b 20 |3.4f... | .13 + |
|00001040| 11 33 78 20 20 11 31 3d | 20 30 20 20 11 34 35 35 |.3x .1=| 0 .455|
|00001050| 35 35 36 20 20 11 33 78 | 20 20 11 31 3d 20 2d 33 |556 .3x| .1= -3|
|00001060| 20 20 11 34 35 35 35 35 | 36 20 20 11 33 78 20 11 | .45555|6 .3x .|
|00001070| 31 3d 20 11 34 76 20 11 | 31 2d 33 00 0c 0d 0a 00 |1= .4v .|1-3.....|
|00001080| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
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|000010e0| 11 34 66 20 20 20 20 20 | 20 11 32 33 11 34 66 0d |.4f | .23.4f.|
|000010f0| 0b 00 11 31 54 68 75 73 | 2c 20 74 68 65 20 65 71 |...1Thus|, the eq|
|00001100| 75 61 74 69 6f 6e 20 68 | 61 73 20 74 77 6f 20 73 |uation h|as two s|
|00001110| 6f 6c 75 74 69 6f 6e 73 | 3a 20 11 34 76 20 11 31 |olutions|: .4v .1|
|00001120| 35 20 61 6e 64 20 11 34 | 76 20 11 31 2d 33 2e 20 |5 and .4|v .1-3. |
|00001130| 20 54 72 79 20 63 68 65 | 63 6b 69 6e 67 20 74 68 | Try che|cking th|
|00001140| 65 73 65 20 0d 0a 00 73 | 6f 6c 75 74 69 6f 6e 73 |ese ...s|olutions|
|00001150| 20 69 6e 20 74 68 65 20 | 6f 72 69 67 69 6e 61 6c | in the |original|
|00001160| 20 65 71 75 61 74 69 6f | 6e 2e 0d 0a 00 53 65 63 | equatio|n....Sec|
|00001170| 74 69 6f 6e 20 31 2e 36 | 20 20 4f 74 68 65 72 20 |tion 1.6| Other |
|00001180| 54 79 70 65 73 20 6f 66 | 20 45 71 75 61 74 69 6f |Types of| Equatio|
|00001190| 6e 73 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |ns... | |
|000011a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000011b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000011c0| 20 20 20 11 32 32 2f 33 | 20 20 20 20 31 2f 33 0d | .22/3| 1/3.|
|000011d0| 0b 00 11 31 46 69 6e 64 | 20 61 6c 6c 20 74 68 65 |...1Find| all the|
|000011e0| 20 72 65 61 6c 20 73 6f | 6c 75 74 69 6f 6e 73 20 | real so|lutions |
|000011f0| 6f 66 20 74 68 65 20 65 | 71 75 61 74 69 6f 6e 20 |of the e|quation |
|00001200| 32 11 33 78 20 20 20 20 | 11 31 2b 20 11 33 78 20 |2.3x |.1+ .3x |
|00001210| 20 20 20 11 31 2d 20 33 | 20 3d 20 30 2e 0d 0a 00 | .1- 3| = 0....|
|00001220| 0d 0b 00 13 12 31 53 4f | 4c 55 54 49 4f 4e 12 30 |.....1SO|LUTION.0|
|00001230| 0d 0a 00 20 20 20 20 20 | 20 20 20 11 32 32 2f 33 |... | .22/3|
|00001240| 20 20 20 20 31 2f 33 0d | 0b 00 20 20 20 20 20 20 | 1/3.|.. |
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|00001270| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001280| 20 20 20 12 31 11 32 47 | 69 76 65 6e 20 65 71 75 | .1.2G|iven equ|
|00001290| 61 74 69 6f 6e 11 31 12 | 30 13 0d 0a 00 20 20 20 |ation.1.|0.... |
|000012a0| 20 11 32 31 2f 33 20 32 | 20 20 20 20 20 31 2f 33 | .21/3 2| 1/3|
|000012b0| 0d 0b 00 20 11 31 32 28 | 11 33 78 20 20 20 11 31 |... .12(|.3x .1|
|000012c0| 29 20 20 2b 20 28 11 33 | 78 20 20 20 11 31 29 20 |) + (.3|x .1) |
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|000012e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 12 31 11 32 | | .1.2|
|000012f0| 57 72 69 74 65 20 69 6e | 20 71 75 61 64 72 61 74 |Write in| quadrat|
|00001300| 69 63 20 66 6f 72 6d 11 | 31 12 30 13 0d 0a 00 20 |ic form.|1.0.... |
|00001310| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 32 32 20 | | .22 |
|00001320| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001330| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001340| 11 31 12 31 20 20 20 20 | 20 20 20 20 20 11 32 31 |.1.1 | .21|
|00001350| 2f 33 20 20 20 20 20 11 | 31 12 30 0d 0b 00 20 20 |/3 .|1.0... |
|00001360| 20 20 20 20 20 20 20 20 | 20 32 11 33 75 20 20 11 | | 2.3u .|
|00001370| 31 2b 20 11 33 75 20 11 | 31 2d 20 33 20 3d 20 30 |1+ .3u .|1- 3 = 0|
|00001380| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001390| 20 20 20 20 20 12 31 11 | 32 52 65 70 6c 61 63 65 | .1.|2Replace|
|000013a0| 20 78 20 20 20 20 62 79 | 20 75 11 31 12 30 13 0d | x by| u.1.0..|
|000013b0| 0a 00 0d 0b 00 20 20 20 | 20 20 20 20 28 32 11 33 |..... | (2.3|
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|000013d0| 20 31 29 20 3d 20 30 20 | 20 20 20 20 20 20 20 20 | 1) = 0 | |
|000013e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 12 31 11 32 | | .1.2|
|000013f0| 46 61 63 74 6f 72 11 31 | 12 30 13 0d 0a 00 20 20 |Factor.1|.0.... |
|00001400| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001410| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001420| 20 20 20 20 20 20 33 0d | 0b 00 20 20 20 20 20 20 | 3.|.. |
|00001430| 20 20 20 20 20 20 20 20 | 20 20 32 11 33 75 20 11 | | 2.3u .|
|00001440| 31 2b 20 33 20 3d 20 30 | 20 20 20 11 34 35 35 36 |1+ 3 = 0| .4556|
|00001450| 20 20 20 11 33 75 20 11 | 31 3d 20 2d 11 34 32 20 | .3u .|1= -.42 |
|00001460| 20 20 20 20 20 11 31 12 | 31 11 32 53 65 74 20 66 | .1.|1.2Set f|
|00001470| 69 72 73 74 20 66 61 63 | 74 6f 72 20 65 71 75 61 |irst fac|tor equa|
|00001480| 6c 20 74 6f 20 30 11 31 | 12 30 0d 0b 00 20 20 20 |l to 0.1|.0... |
|00001490| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000014a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000014b0| 20 20 20 20 20 32 20 20 | 20 20 20 20 20 20 20 20 | 2 | |
|000014c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
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|000014e0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|000014f0| 20 20 11 33 75 20 11 31 | 2d 20 31 20 3d 20 30 20 | .3u .1|- 1 = 0 |
|00001500| 20 20 11 34 35 35 36 20 | 20 20 11 33 75 20 11 31 | .4556 | .3u .1|
|00001510| 3d 20 31 20 20 20 20 20 | 20 20 12 31 11 32 53 65 |= 1 | .1.2Se|
|00001520| 74 20 73 65 63 6f 6e 64 | 20 66 61 63 74 6f 72 20 |t second| factor |
|00001530| 65 71 75 61 6c 20 74 6f | 20 30 11 31 12 30 13 0d |equal to| 0.1.0..|
|00001540| 0a 00 0d 0b 00 4e 6f 77 | 2c 20 75 73 69 6e 67 20 |.....Now|, using |
|00001550| 74 68 65 20 11 33 75 11 | 31 2d 73 6f 6c 75 74 69 |the .3u.|1-soluti|
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|00001570| 31 2c 20 77 65 20 6f 62 | 74 61 69 6e 20 74 68 65 |1, we ob|tain the|
|00001580| 20 66 6f 6c 6c 6f 77 69 | 6e 67 20 11 33 78 11 31 | followi|ng .3x.1|
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|000015a0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|000015b0| 20 33 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 | 3 | .2|
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|000015d0| 20 20 20 20 20 20 20 20 | 20 11 34 28 20 11 31 33 | | .4( .13|
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|00001600| 11 31 3d 20 2d 11 34 32 | 20 20 20 20 35 35 36 20 |.1= -.42| 556 |
|00001610| 20 20 20 11 33 78 20 20 | 20 20 11 31 3d 20 2d 11 | .3x | .1= -.|
|00001620| 34 32 20 20 20 20 35 35 | 36 20 20 20 20 11 33 78 |42 55|6 .3x|
|00001630| 20 11 31 3d 20 11 34 21 | 11 31 2d 11 34 32 21 20 | .1= .4!|.1-.42! |
|00001640| 20 11 31 3d 20 2d 11 34 | 32 32 0d 0b 00 20 20 20 | .1= -.4|22... |
|00001650| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 31 32 | | .12|
|00001660| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001670| 20 20 20 32 20 20 20 20 | 20 20 20 20 20 20 20 20 | 2 | |
|00001680| 20 20 20 11 34 39 20 11 | 31 32 11 34 30 20 20 20 | .49 .|12.40 |
|00001690| 20 20 20 11 31 38 13 0d | 0a 00 20 20 20 20 20 20 | .18..|.. |
|000016a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
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|00001710| 20 20 20 11 33 78 20 11 | 31 3d 20 28 31 29 20 20 | .3x .|1= (1) |
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|00001740| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001750| 20 20 20 20 20 32 37 0d | 0b 00 54 68 75 73 2c 20 | 27.|..Thus, |
|00001760| 74 68 65 20 67 69 76 65 | 6e 20 65 71 75 61 74 69 |the give|n equati|
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|000017f0| 20 74 68 65 20 6f 72 69 | 67 69 6e 61 6c 20 65 71 | the ori|ginal eq|
|00001800| 75 61 74 69 6f 6e 2e 0d | 0a 00 53 65 63 74 69 6f |uation..|..Sectio|
|00001810| 6e 20 31 2e 36 20 20 4f | 74 68 65 72 20 54 79 70 |n 1.6 O|ther Typ|
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|00001860| 20 20 20 0d 0b 00 11 31 | 53 6f 6c 76 65 20 74 68 | ....1|Solve th|
|00001870| 65 20 66 6f 6c 6c 6f 77 | 69 6e 67 20 65 71 75 61 |e follow|ing equa|
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|00001990| 20 33 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | 3 | |
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|00001a80| 20 20 20 20 20 20 20 11 | 31 12 31 11 32 54 72 69 | .|1.1.2Tri|
|00001a90| 61 6c 20 73 6f 6c 75 74 | 69 6f 6e 11 31 12 30 0d |al solut|ion.1.0.|
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|00001ae0| 0d 0a 00 4e 6f 77 20 77 | 65 20 6d 75 73 74 20 63 |...Now w|e must c|
|00001af0| 68 65 63 6b 20 74 68 69 | 73 20 73 6f 6c 75 74 69 |heck thi|s soluti|
|00001b00| 6f 6e 20 69 6e 20 74 68 | 65 20 6f 72 69 67 69 6e |on in th|e origin|
|00001b10| 61 6c 20 65 71 75 61 74 | 69 6f 6e 2e 0d 0a 00 20 |al equat|ion.... |
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|00001b60| 20 20 12 31 11 32 47 69 | 76 65 6e 20 65 71 75 61 | .1.2Gi|ven equa|
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|00001be0| 20 20 20 12 31 11 32 52 | 65 70 6c 61 63 65 20 7a | .1.2R|eplace z|
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|00001c50| 20 20 20 20 20 20 11 34 | 44 32 32 32 32 32 20 11 | .4|D22222 .|
|00001c60| 31 12 31 3f 12 30 0d 0b | 00 20 20 20 20 20 20 20 |1.1?.0..|. |
|00001c70| 20 11 34 53 20 11 31 37 | 20 2b 20 32 20 3d 20 33 | .4S .17| + 2 = 3|
|00001c80| 20 20 20 20 13 0d 0a 00 | 20 20 20 20 20 20 20 20 | ....| |
|00001c90| 20 20 20 20 11 34 44 32 | 0d 0b 00 20 20 20 20 20 | .4D2|... |
|00001ca0| 20 20 20 20 20 20 11 34 | 53 20 11 31 39 20 3d 20 | .4|S .19 = |
|00001cb0| 33 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |3 | |
|00001cc0| 20 20 20 20 20 20 20 12 | 31 11 32 53 6f 6c 75 74 | .|1.2Solut|
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|00001ce0| 0a 00 0d 0b 00 54 68 65 | 72 65 66 6f 72 65 2c 20 |.....The|refore, |
|00001cf0| 74 68 65 20 65 71 75 61 | 74 69 6f 6e 20 68 61 73 |the equa|tion has|
|00001d00| 20 6f 6e 65 20 73 6f 6c | 75 74 69 6f 6e 3a 20 11 | one sol|ution: .|
|00001d10| 33 7a 20 11 31 3d 20 2d | 32 2f 33 2e 0d 0a 00 53 |3z .1= -|2/3....S|
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|00001d30| 72 20 54 79 70 65 73 20 | 6f 66 20 45 71 75 61 74 |r Types |of Equat|
|00001d40| 69 6f 6e 73 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |ions... | |
|00001d50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001d60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001d70| 20 11 32 35 2f 32 0d 0b | 00 11 31 46 69 6e 64 20 | .25/2..|..1Find |
|00001d80| 61 6c 6c 20 73 6f 6c 75 | 74 69 6f 6e 73 20 6f 66 |all solu|tions of|
|00001d90| 20 74 68 65 20 65 71 75 | 61 74 69 6f 6e 20 28 11 | the equ|ation (.|
|00001da0| 33 78 20 11 31 2b 20 32 | 29 20 20 20 20 2d 20 33 |3x .1+ 2|) - 3|
|00001db0| 32 20 3d 20 30 2e 0d 0a | 00 0d 0b 00 13 12 31 53 |2 = 0...|......1S|
|00001dc0| 4f 4c 55 54 49 4f 4e 12 | 30 0d 0a 00 0d 0b 00 20 |OLUTION.|0...... |
|00001dd0| 20 20 20 20 20 20 20 20 | 20 11 32 35 2f 32 0d 0b | | .25/2..|
|00001de0| 00 20 20 20 11 31 28 11 | 33 78 20 11 31 2b 20 32 |. .1(.|3x .1+ 2|
|00001df0| 29 20 20 20 20 2d 20 33 | 32 20 3d 20 30 20 20 20 |) - 3|2 = 0 |
|00001e00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001e10| 12 31 11 32 47 69 76 65 | 6e 20 65 71 75 61 74 69 |.1.2Give|n equati|
|00001e20| 6f 6e 11 31 12 30 11 32 | 13 0d 0a 00 20 20 20 20 |on.1.0.2|.... |
|00001e30| 20 20 20 20 20 20 20 20 | 20 20 20 35 2f 32 0d 0b | | 5/2..|
|00001e40| 00 20 20 20 20 20 20 20 | 20 11 31 28 11 33 78 20 |. | .1(.3x |
|00001e50| 11 31 2b 20 32 29 20 20 | 20 20 3d 20 33 32 20 20 |.1+ 2) | = 32 |
|00001e60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001e70| 12 31 11 32 41 64 64 20 | 33 32 20 74 6f 20 62 6f |.1.2Add |32 to bo|
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|00001e90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001ea0| 20 20 20 20 20 20 20 11 | 32 32 2f 35 0d 0b 00 20 | .|22/5... |
|00001eb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 33 78 20 | | .3x |
|00001ec0| 11 31 2b 20 32 20 3d 20 | 33 32 20 20 20 20 20 20 |.1+ 2 = |32 |
|00001ed0| 20 20 20 20 20 20 20 20 | 20 20 20 20 12 31 11 32 | | .1.2|
|00001ee0| 52 61 69 73 65 20 62 6f | 74 68 20 73 69 64 65 73 |Raise bo|th sides|
|00001ef0| 20 74 6f 20 32 2f 35 20 | 70 6f 77 65 72 11 31 12 | to 2/5 |power.1.|
|00001f00| 30 13 0d 0a 00 0d 0b 00 | 20 20 20 20 20 20 20 20 |0.......| |
|00001f10| 20 20 20 20 20 11 33 78 | 20 11 31 2b 20 32 20 3d | .3x| .1+ 2 =|
|00001f20| 20 34 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | 4 | |
|00001f30| 20 20 20 20 20 12 31 11 | 32 53 69 6d 70 6c 69 66 | .1.|2Simplif|
|00001f40| 79 11 31 12 30 13 0d 0a | 00 0d 0b 00 20 20 20 20 |y.1.0...|.... |
|00001f50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 33 78 | | .3x|
|00001f60| 20 11 31 3d 20 32 20 20 | 20 20 20 20 20 20 20 20 | .1= 2 | |
|00001f70| 20 20 20 20 20 20 20 20 | 20 12 31 11 32 53 75 62 | | .1.2Sub|
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|00001fc0| 65 20 73 6f 6c 75 74 69 | 6f 6e 3a 20 32 2e 20 20 |e soluti|on: 2. |
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|00001fe0| 73 20 73 6f 6c 75 74 69 | 6f 6e 20 69 6e 20 0d 0a |s soluti|on in ..|
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|00002050| 20 65 71 75 61 74 69 6f | 6e 20 67 69 76 65 6e 20 | equatio|n given |
|00002060| 62 65 6c 6f 77 2e 0d 0a | 00 0d 0b 00 20 20 20 20 |below...|.... |
|00002070| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002080| 20 20 20 20 20 20 20 20 | 11 33 78 20 20 20 20 20 | |.3x |
|00002090| 20 11 31 34 11 33 78 0d | 0b 00 20 20 20 20 20 20 | .14.3x.|.. |
|000020a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000020b0| 20 20 20 20 11 34 32 32 | 32 32 32 20 11 31 2b 20 | .422|222 .1+ |
|000020c0| 11 34 32 32 32 32 32 20 | 11 31 3d 20 2d 31 0d 0b |.422222 |.1= -1..|
|000020d0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|000020e0| 20 20 20 20 20 20 20 20 | 20 20 20 11 33 78 20 11 | | .3x .|
|000020f0| 31 2d 20 31 20 20 20 11 | 33 78 20 11 31 2b 20 32 |1- 1 .|3x .1+ 2|
|00002100| 0d 0a 00 0d 0b 00 13 12 | 31 53 4f 4c 55 54 49 4f |........|1SOLUTIO|
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|00002140| 20 69 6e 20 74 68 65 20 | 6f 72 69 67 69 6e 61 6c | in the |original|
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|00002160| 20 4c 43 44 0d 0a 00 77 | 68 69 63 68 20 69 73 20 | LCD...w|hich is |
|00002170| 28 11 33 78 20 11 31 2d | 20 31 29 28 11 33 78 20 |(.3x .1-| 1)(.3x |
|00002180| 11 31 2b 20 32 29 2e 13 | 0d 0a 00 0d 0b 00 20 20 |.1+ 2)..|...... |
|00002190| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 34 | | .4|
|000021a0| 28 20 20 20 20 20 29 20 | 20 20 20 20 20 20 20 20 |( ) | |
|000021b0| 20 20 20 20 20 20 20 20 | 28 20 20 20 20 20 29 0d | |( ).|
|000021c0| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|000021d0| 20 20 21 20 20 11 33 78 | 20 20 11 34 21 20 20 20 | ! .3x| .4! |
|000021e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 21 20 | | ! |
|000021f0| 11 31 34 11 33 78 20 20 | 11 34 21 0d 0b 00 20 20 |.14.3x |.4!... |
|00002200| 11 31 28 11 33 78 20 11 | 31 2d 20 31 29 28 11 33 |.1(.3x .|1- 1)(.3|
|00002210| 78 20 11 31 2b 20 32 29 | 11 34 21 32 32 32 32 32 |x .1+ 2)|.4!22222|
|00002220| 21 20 11 31 2b 20 28 11 | 33 78 20 11 31 2d 20 31 |! .1+ (.|3x .1- 1|
|00002230| 29 28 11 33 78 20 11 31 | 2b 20 32 29 11 34 21 32 |)(.3x .1|+ 2).4!2|
|00002240| 32 32 32 32 21 20 11 31 | 3d 20 28 11 33 78 20 11 |2222! .1|= (.3x .|
|00002250| 31 2d 20 31 29 28 11 33 | 78 20 11 31 2b 20 32 29 |1- 1)(.3|x .1+ 2)|
|00002260| 28 2d 31 29 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |(-1)... | |
|00002270| 20 20 20 20 20 20 20 11 | 34 21 11 33 78 20 11 31 | .|4!.3x .1|
|00002280| 2d 20 31 11 34 21 20 20 | 20 20 20 20 20 20 20 20 |- 1.4! | |
|00002290| 20 20 20 20 20 20 20 21 | 11 33 78 20 11 31 2b 20 | !|.3x .1+ |
|000022a0| 32 11 34 21 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |2.4!... | |
|000022b0| 20 20 20 20 20 20 20 39 | 20 20 20 20 20 30 20 20 | 9| 0 |
|000022c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 39 | | 9|
|000022d0| 20 20 20 20 20 30 20 20 | 20 20 20 20 20 20 20 20 | 0 | |
|000022e0| 20 20 20 20 20 20 20 20 | 20 20 20 11 31 13 0d 0a | | .1...|
|000022f0| 00 0d 0b 00 4e 65 78 74 | 2c 20 77 65 20 73 69 6d |....Next|, we sim|
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|00002310| 6f 6e 20 61 6e 64 20 73 | 6f 6c 76 65 20 66 6f 72 |on and s|olve for|
|00002320| 20 11 33 78 11 31 2e 13 | 0d 0a 00 0d 0b 00 20 20 | .3x.1..|...... |
|00002330| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002340| 20 20 20 20 20 20 20 11 | 32 32 0d 0b 00 11 31 28 | .|22....1(|
|00002350| 11 33 78 20 11 31 2b 20 | 32 29 11 33 78 20 11 31 |.3x .1+ |2).3x .1|
|00002360| 2b 20 28 11 33 78 20 11 | 31 2d 20 31 29 34 11 33 |+ (.3x .|1- 1)4.3|
|00002370| 78 20 11 31 3d 20 28 11 | 33 78 20 20 11 31 2b 20 |x .1= (.|3x .1+ |
|00002380| 11 33 78 20 11 31 2d 20 | 32 29 28 2d 31 29 2c 20 |.3x .1- |2)(-1), |
|00002390| 20 11 33 78 20 11 34 3d | 20 11 31 31 2c 20 2d 32 | .3x .4=| .11, -2|
|000023a0| 13 0d 0a 00 0d 0b 00 20 | 20 20 11 32 32 20 20 20 |....... | .22 |
|000023b0| 20 20 20 20 20 20 20 32 | 20 20 20 20 20 20 20 20 | 2| |
|000023c0| 20 20 32 0d 0b 00 20 20 | 11 33 78 20 20 11 31 2b | 2... |.3x .1+|
|000023d0| 20 32 11 33 78 20 11 31 | 2b 20 34 11 33 78 20 20 | 2.3x .1|+ 4.3x |
|000023e0| 11 31 2d 20 34 11 33 78 | 20 11 31 3d 20 2d 11 33 |.1- 4.3x| .1= -.3|
|000023f0| 78 20 20 11 31 2d 20 11 | 33 78 20 11 31 2b 20 32 |x .1- .|3x .1+ 2|
|00002400| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 12 | | .|
|00002410| 31 11 32 52 65 6d 6f 76 | 65 20 70 61 72 65 6e 74 |1.2Remov|e parent|
|00002420| 68 65 73 65 73 11 31 12 | 30 11 32 13 0d 0a 00 0d |heses.1.|0.2.....|
|00002430| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 32 0d 0b |.. | 2..|
|00002440| 00 20 20 20 20 20 20 20 | 20 20 11 31 36 11 33 78 |. | .16.3x|
|00002450| 20 20 11 31 2d 20 11 33 | 78 20 11 31 2d 20 32 20 | .1- .3|x .1- 2 |
|00002460| 3d 20 30 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |= 0 | |
|00002470| 20 20 20 20 20 20 20 20 | 20 20 20 20 12 31 11 32 | | .1.2|
|00002480| 53 74 61 6e 64 61 72 64 | 20 66 6f 72 6d 11 31 12 |Standard| form.1.|
|00002490| 30 0d 0a 00 0d 0a 00 20 | 20 20 20 28 33 11 33 78 |0...... | (3.3x|
|000024a0| 20 11 31 2d 20 32 29 28 | 32 11 33 78 20 11 31 2b | .1- 2)(|2.3x .1+|
|000024b0| 20 31 29 20 3d 20 30 20 | 20 20 20 20 20 20 20 20 | 1) = 0 | |
|000024c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000024d0| 12 31 11 32 46 61 63 74 | 6f 72 11 31 12 30 11 32 |.1.2Fact|or.1.0.2|
|000024e0| 13 0d 0a 00 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |....... | |
|000024f0| 20 20 20 20 20 11 31 33 | 11 33 78 20 11 31 2d 20 | .13|.3x .1- |
|00002500| 32 20 3d 20 30 20 20 11 | 34 35 35 36 20 20 11 33 |2 = 0 .|4556 .3|
|00002510| 78 20 11 31 3d 20 32 2f | 33 20 20 20 20 20 20 20 |x .1= 2/|3 |
|00002520| 20 20 20 20 12 31 11 32 | 53 65 74 20 31 73 74 20 | .1.2|Set 1st |
|00002530| 66 61 63 74 6f 72 20 65 | 71 75 61 6c 20 74 6f 20 |factor e|qual to |
|00002540| 30 11 31 12 30 13 0d 0a | 00 0d 0a 00 20 20 20 20 |0.1.0...|.... |
|00002550| 20 20 20 20 20 20 20 20 | 20 20 32 11 33 78 20 11 | | 2.3x .|
|00002560| 31 2b 20 31 20 3d 20 30 | 20 20 11 34 35 35 36 20 |1+ 1 = 0| .4556 |
|00002570| 20 11 33 78 20 11 31 3d | 20 2d 31 2f 32 20 20 20 | .3x .1=| -1/2 |
|00002580| 20 20 20 20 20 20 20 12 | 31 11 32 53 65 74 20 32 | .|1.2Set 2|
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|000025a0| 74 6f 20 30 11 31 12 30 | 11 32 13 0d 0a 00 0d 0a |to 0.1.0|.2......|
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|000025c0| 61 74 69 6f 6e 20 68 61 | 73 20 74 77 6f 20 73 6f |ation ha|s two so|
|000025d0| 6c 75 74 69 6f 6e 73 3a | 20 32 2f 33 20 61 6e 64 |lutions:| 2/3 and|
|000025e0| 20 2d 31 2f 32 2e 20 20 | 54 72 79 20 63 68 65 63 | -1/2. |Try chec|
|000025f0| 6b 69 6e 67 20 74 68 65 | 73 65 20 0d 0a 00 73 6f |king the|se ...so|
|00002600| 6c 75 74 69 6f 6e 73 20 | 69 6e 20 74 68 65 20 6f |lutions |in the o|
|00002610| 72 69 67 69 6e 61 6c 20 | 65 71 75 61 74 69 6f 6e |riginal |equation|
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|00002630| 20 4f 74 68 65 72 20 54 | 79 70 65 73 20 6f 66 20 | Other T|ypes of |
|00002640| 45 71 75 61 74 69 6f 6e | 73 0d 0b 00 20 20 20 20 |Equation|s... |
|00002650| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002660| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002670| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00002680| 32 32 0d 0b 00 11 31 46 | 69 6e 64 20 74 68 65 20 |22....1F|ind the |
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|000026b0| 11 33 78 20 11 31 2b 20 | 33 7c 20 3d 20 11 33 78 |.3x .1+ |3| = .3x|
|000026c0| 20 20 11 31 2d 20 33 2e | 0d 0a 00 0d 0a 00 13 12 | .1- 3.|........|
|000026d0| 31 53 4f 4c 55 54 49 4f | 4e 12 30 0d 0a 00 0d 0b |1SOLUTIO|N.0.....|
|000026e0| 00 53 69 6e 63 65 20 74 | 68 65 20 76 61 72 69 61 |.Since t|he varia|
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|00002730| 00 6f 72 20 6e 65 67 61 | 74 69 76 65 2c 20 77 65 |.or nega|tive, we|
|00002740| 20 6d 75 73 74 20 73 6f | 6c 76 65 20 74 77 6f 20 | must so|lve two |
|00002750| 65 71 75 61 74 69 6f 6e | 73 2e 0d 0a 00 20 20 20 |equation|s.... |
|00002760| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 32 32 | | .22|
|00002770| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002780| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002790| 20 20 20 20 20 20 20 32 | 0d 0b 00 20 20 20 20 20 | 2|... |
|000027a0| 20 20 11 33 78 20 11 31 | 2b 20 33 20 3d 20 11 33 | .3x .1|+ 3 = .3|
|000027b0| 78 20 20 11 31 2d 20 33 | 20 20 20 20 20 20 20 20 |x .1- 3| |
|000027c0| 20 20 61 6e 64 20 20 20 | 20 20 20 20 20 20 20 2d | and | -|
|000027d0| 28 11 33 78 20 11 31 2b | 20 33 29 20 3d 20 11 33 |(.3x .1+| 3) = .3|
|000027e0| 78 20 20 11 31 2d 20 33 | 13 0d 0a 00 0d 0b 00 46 |x .1- 3|.......F|
|000027f0| 69 72 73 74 20 65 71 75 | 61 74 69 6f 6e 0d 0b 00 |irst equ|ation...|
|00002800| 11 34 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |.4222222|22222222|
|00002810| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|00002820| 20 20 20 20 20 20 20 20 | 11 32 32 0d 0b 00 20 20 | |.22... |
|00002830| 20 20 20 20 20 20 20 20 | 20 20 11 33 78 20 11 31 | | .3x .1|
|00002840| 2b 20 33 20 3d 20 11 33 | 78 20 20 11 31 2d 20 33 |+ 3 = .3|x .1- 3|
|00002850| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002860| 12 31 11 32 55 73 65 20 | 70 6f 73 69 74 69 76 65 |.1.2Use |positive|
|00002870| 20 65 78 70 72 65 73 73 | 69 6f 6e 11 31 12 30 13 | express|ion.1.0.|
|00002880| 0d 0a 00 20 20 20 20 20 | 20 20 20 11 32 32 0d 0b |... | .22..|
|00002890| 00 20 20 20 20 20 20 20 | 11 33 78 20 20 11 31 2d |. |.3x .1-|
|000028a0| 20 11 33 78 20 11 31 2d | 20 36 20 3d 20 30 20 20 | .3x .1-| 6 = 0 |
|000028b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000028c0| 20 20 20 12 31 11 32 53 | 74 61 6e 64 61 72 64 20 | .1.2S|tandard |
|000028d0| 66 6f 72 6d 11 31 12 30 | 13 0d 0a 00 0d 0b 00 20 |form.1.0|....... |
|000028e0| 20 20 28 11 33 78 20 11 | 31 2b 20 32 29 28 11 33 | (.3x .|1+ 2)(.3|
|000028f0| 78 20 11 31 2d 20 33 29 | 20 3d 20 30 20 20 20 20 |x .1- 3)| = 0 |
|00002900| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002910| 20 12 31 11 32 46 61 63 | 74 6f 72 11 31 12 30 13 | .1.2Fac|tor.1.0.|
|00002920| 0d 0a 00 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |...... | |
|00002930| 20 20 11 33 78 20 11 31 | 2b 20 32 20 3d 20 30 20 | .3x .1|+ 2 = 0 |
|00002940| 20 11 34 35 35 36 20 20 | 11 33 78 20 11 31 3d 20 | .4556 |.3x .1= |
|00002950| 2d 32 20 20 20 20 20 20 | 20 20 12 31 11 32 53 65 |-2 | .1.2Se|
|00002960| 74 20 31 73 74 20 66 61 | 63 74 6f 72 20 65 71 75 |t 1st fa|ctor equ|
|00002970| 61 6c 20 74 6f 20 30 11 | 31 12 30 13 0d 0a 00 0d |al to 0.|1.0.....|
|00002980| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 11 33 |.. | .3|
|00002990| 78 20 11 31 2d 20 33 20 | 3d 20 30 20 20 11 34 35 |x .1- 3 |= 0 .45|
|000029a0| 35 36 20 20 11 33 78 20 | 11 31 3d 20 33 20 20 20 |56 .3x |.1= 3 |
|000029b0| 20 20 20 20 20 20 12 31 | 11 32 53 65 74 20 32 6e | .1|.2Set 2n|
|000029c0| 64 20 66 61 63 74 6f 72 | 20 65 71 75 61 6c 20 74 |d factor| equal t|
|000029d0| 6f 20 30 11 31 12 30 00 | 0c 0d 0a 00 0d 0b 00 53 |o 0.1.0.|.......S|
|000029e0| 65 63 6f 6e 64 20 65 71 | 75 61 74 69 6f 6e 0d 0b |econd eq|uation..|
|000029f0| 00 11 34 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |..422222|22222222|
|00002a00| 32 32 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |22... | |
|00002a10| 20 20 20 20 20 20 20 20 | 20 20 11 32 32 0d 0b 00 | | .22...|
|00002a20| 20 20 20 20 20 20 20 20 | 20 11 31 2d 28 11 33 78 | | .1-(.3x|
|00002a30| 20 11 31 2b 20 33 29 20 | 3d 20 11 33 78 20 20 11 | .1+ 3) |= .3x .|
|00002a40| 31 2d 20 33 20 20 20 20 | 20 20 20 20 20 20 20 20 |1- 3 | |
|00002a50| 20 20 20 20 12 31 11 32 | 55 73 65 20 6e 65 67 61 | .1.2|Use nega|
|00002a60| 74 69 76 65 20 65 78 70 | 72 65 73 73 69 6f 6e 11 |tive exp|ression.|
|00002a70| 31 12 30 13 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |1.0.... | |
|00002a80| 20 20 20 11 32 32 0d 0b | 00 20 20 20 20 20 20 20 | .22..|. |
|00002a90| 20 20 20 20 11 33 78 20 | 20 11 31 2b 20 11 33 78 | .3x | .1+ .3x|
|00002aa0| 20 11 31 3d 20 30 20 20 | 20 20 20 20 20 20 20 20 | .1= 0 | |
|00002ab0| 20 20 20 20 20 20 20 20 | 20 20 20 12 31 11 32 53 | | .1.2S|
|00002ac0| 74 61 6e 64 61 72 64 20 | 66 6f 72 6d 11 31 12 30 |tandard |form.1.0|
|00002ad0| 13 0d 0a 00 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |....... | |
|00002ae0| 11 33 78 11 31 28 11 33 | 78 20 11 31 2b 20 31 29 |.3x.1(.3|x .1+ 1)|
|00002af0| 20 3d 20 30 20 20 20 20 | 20 20 20 20 20 20 20 20 | = 0 | |
|00002b00| 20 20 20 20 20 20 20 20 | 20 12 31 11 32 46 61 63 | | .1.2Fac|
|00002b10| 74 6f 72 11 31 12 30 13 | 0d 0a 00 0d 0b 00 20 20 |tor.1.0.|...... |
|00002b20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 33 | | .3|
|00002b30| 78 20 11 31 3d 20 30 20 | 20 20 20 20 20 20 20 20 |x .1= 0 | |
|00002b40| 20 20 20 20 20 20 20 20 | 20 20 20 20 12 31 11 32 | | .1.2|
|00002b50| 53 65 74 20 31 73 74 20 | 66 61 63 74 6f 72 20 65 |Set 1st |factor e|
|00002b60| 71 75 61 6c 20 74 6f 20 | 30 11 31 12 30 13 0d 0a |qual to |0.1.0...|
|00002b70| 00 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |.... | |
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|00002bb0| 32 6e 64 20 66 61 63 74 | 6f 72 20 65 71 75 61 6c |2nd fact|or equal|
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|00002c60| 61 20 63 65 72 74 61 69 | 6e 20 70 72 6f 64 75 63 |a certai|n produc|
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|00002d20| 33 70 20 11 31 69 73 20 | 74 68 65 20 70 72 69 63 |3p .1is |the pric|
|00002d30| 65 20 70 65 72 20 75 6e | 69 74 2e 0d 0a 00 46 69 |e per un|it....Fi|
|00002d40| 6e 64 20 74 68 65 20 64 | 65 6d 61 6e 64 20 69 66 |nd the d|emand if|
|00002d50| 20 74 68 65 20 70 72 69 | 63 65 20 69 73 20 73 65 | the pri|ce is se|
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|00002e40| 11 31 30 2e 30 30 30 31 | 11 33 78 20 11 31 2b 20 |.10.0001|.3x .1+ |
|00002e50| 31 20 20 20 20 20 20 20 | 20 20 20 20 20 12 31 11 |1 | .1.|
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|00002e70| 39 2e 39 35 11 31 12 30 | 13 0d 0a 00 20 20 11 34 |9.95.1.0|.... .4|
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|00002eb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002ec0| 20 20 20 20 12 31 11 32 | 49 73 6f 6c 61 74 65 20 | .1.2|Isolate |
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|00002f00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
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|00003090| 00 11 31 53 6f 6c 76 65 | 20 74 68 65 20 66 6f 6c |..1Solve| the fol|
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|000030c0| 20 20 20 20 20 20 20 20 | 20 20 0d 0a 00 20 20 20 | | ... |
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|00003210| 20 20 20 20 20 20 20 11 | 31 12 31 11 32 53 71 75 | .|1.1.2Squ|
|00003220| 61 72 65 20 62 6f 74 68 | 20 73 69 64 65 73 11 31 |are both| sides.1|
|00003230| 12 30 0d 0b 00 20 20 20 | 20 20 20 20 11 34 39 20 |.0... | .49 |
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|000032c0| 2d 20 34 11 33 74 20 11 | 31 2b 20 31 13 0d 0a 00 |- 4.3t .|1+ 1....|
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|00003340| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
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|00003360| 28 11 33 74 20 11 31 2d | 20 31 29 20 20 20 20 20 |(.3t .1-| 1) |
|00003370| 20 20 20 20 20 20 12 31 | 11 32 46 61 63 74 6f 72 | .1|.2Factor|
|00003380| 11 31 12 30 13 0d 0a 00 | 20 20 20 20 20 20 20 20 |.1.0....| |
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|000033a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 31 0d 0b | | 1..|
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|000033f0| 32 53 65 74 20 66 69 72 | 73 74 20 66 61 63 74 6f |2Set fir|st facto|
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|000034f0| 73 20 61 20 76 61 6c 69 | 64 20 73 6f 6c 75 74 69 |s a vali|d soluti|
|00003500| 6f 6e 2e 20 20 54 68 65 | 72 65 66 6f 72 65 2c 20 |on. The|refore, |
|00003510| 74 68 65 20 67 69 76 65 | 6e 0d 0a 00 65 71 75 61 |the give|n...equa|
|00003520| 74 69 6f 6e 20 68 61 73 | 20 6f 6e 6c 79 20 6f 6e |tion has| only on|
|00003530| 65 20 73 6f 6c 75 74 69 | 6f 6e 2e 0d 0a 00 53 65 |e soluti|on....Se|
|00003540| 63 74 69 6f 6e 20 31 2e | 36 20 20 4f 74 68 65 72 |ction 1.|6 Other|
|00003550| 20 54 79 70 65 73 20 6f | 66 20 45 71 75 61 74 69 | Types o|f Equati|
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|00003590| 20 0d 0b 00 11 31 53 6f | 6c 76 65 20 74 68 65 20 | ....1So|lve the |
|000035a0| 66 6f 6c 6c 6f 77 69 6e | 67 20 65 71 75 61 74 69 |followin|g equati|
|000035b0| 6f 6e 20 66 6f 72 20 11 | 33 79 11 31 2e 20 20 20 |on for .|3y.1. |
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|00003710| 29 20 20 3d 20 28 33 20 | 2d 20 11 34 53 20 11 31 |) = (3 |- .4S .1|
|00003720| 35 11 33 79 11 31 29 20 | 20 20 20 20 20 20 20 20 |5.3y.1) | |
|00003730| 20 20 20 20 20 20 20 20 | 20 20 12 31 11 32 53 71 | | .1.2Sq|
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|000038c0| 20 20 20 20 20 31 30 30 | 20 3d 20 33 36 28 35 11 | 100| = 36(5.|
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|00003970| 20 20 20 20 20 20 20 20 | 20 11 31 12 31 11 32 54 | | .1.1.2T|
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|000039e0| 00 41 20 63 68 65 63 6b | 20 77 69 74 68 20 73 68 |.A check| with sh|
|000039f0| 6f 77 20 74 68 61 74 20 | 11 33 79 20 11 31 3d 20 |ow that |.3y .1= |
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+--------+-------------------------+-------------------------+--------+--------+
