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%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Mar 27 14:51:48 1997}
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\begin{document}


\subsection{Solve Exact and Numeric\hrulefill \label{Solve Exact and Numeric}
}

As with evaluation, when you solve an expression in \textit{Scientific
Notebook,} Maple returns an exact or symbolic answer whenever appropriate.
Otherwise, it returns a numerical approximation. You can use the Solve
Numeric command to force a numerical result for any solution.

You can solve equations with one or more variables. You can solve
inequalities with Solve Exact. And you can solve a system of equations if
you place the equations in a matrix cell, and then apply the Solve Exact
command to the matrix. These examples illustrate how to solve expressions in 
\textit{Scientific Notebook.}

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Solve Exact\ 
$3x+5\leq 5x-3$}

\begin{enumerate}
\item  Click\FRAME{itbpF}{20.125pt}{20.125pt}{2pt}{}{}{text.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 20.125pt;height 20.125pt;depth
2pt;original-width 16.0625pt;original-height 16.0625pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'text.wmf';file-properties
"XNPEU";}}or, from the Insert menu, choose Math to start mathematics.

\item  Type \textbf{3x+5}.

\item  From the Common Symbols toolbar, click\FRAME{itbpF}{20.75pt}{20.0625pt%
}{2pt}{}{}{lessthan.wmf}{\special{language "Scientific Word";type
"GRAPHIC";maintain-aspect-ratio TRUE;display "PICT";valid_file "F";width
20.75pt;height 20.0625pt;depth 2pt;original-width 19.5625pt;original-height
18.8125pt;cropleft "0";croptop "1.0079";cropright "1.0025";cropbottom
"0";filename 'lessthan.wmf';file-properties "XNPEUR";}}.

\item  Type \textbf{5x-3}.

\item  Click\FRAME{itbpF}{21.0625pt}{21.0625pt}{2pt}{}{}{solve.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 21.0625pt;height 21.0625pt;depth
2pt;original-width 18.8125pt;original-height 18.8125pt;cropleft "0";croptop
"1.0079";cropright "1.0079";cropbottom "0";filename
'solve.wmf';file-properties "XNPEU";}}or, from the Maple menu, choose Solve
and then choose Exact. On your screen, you see this solution: \ \medskip 
\[
\fbox{%
\begin{tabular}{lllll}
\rule[-0.1in]{0in}{0.3in} &  & $3x+5\leq 5x-3$, Solution is : $\left\{ 4\leq
x\right\} $ & \rule[-0.1in]{0in}{0.3in} & 
\end{tabular}
}
\]
\medskip 
\end{enumerate}

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Solve Exact\ 
$2x+3y=1$}

\begin{enumerate}
\item  Click\FRAME{itbpF}{20.125pt}{20.125pt}{2pt}{}{}{text.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 20.125pt;height 20.125pt;depth
2pt;original-width 16.0625pt;original-height 16.0625pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'text.wmf';file-properties
"XNPEU";}}or, from the Insert menu, choose Math to start mathematics.

\item  Type \textbf{2x+3y=1}.

Remember that you don't need to enter spaces because \textit{Scientific
Notebook} spaces the expression correctly.

\item  Click\FRAME{itbpF}{21.0625pt}{21.0625pt}{2pt}{}{}{solve.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 21.0625pt;height 21.0625pt;depth
2pt;original-width 18.8125pt;original-height 18.8125pt;cropleft "0";croptop
"1.0079";cropright "1.0079";cropbottom "0";filename
'solve.wmf';file-properties "XNPEU";}}or, from the Maple menu, choose Solve
and then choose Exact.

\item  In the Solution Variables box, enter \textbf{x} and choose OK. Maple
presents this solution: \medskip 
\[
\fbox{%
\begin{tabular}{lllll}
\rule[-0.1in]{0in}{0.3in} &  & $2x+3y=1$, Solution is : $\left\{ x=-\frac{3}{%
2}y+\frac{1}{2}\right\} $ & \rule[-0.1in]{0in}{0.3in} & 
\end{tabular}
}
\]
\end{enumerate}

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Solve
Numeric \ $x^{2}-2=0$}

\begin{enumerate}
\item  Click\FRAME{itbpF}{20.125pt}{20.125pt}{2pt}{}{}{text.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 20.125pt;height 20.125pt;depth
2pt;original-width 16.0625pt;original-height 16.0625pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'text.wmf';file-properties
"XNPEU";}}or, from the Insert menu, choose Math to start mathematics.

\item  Type \textbf{x}, click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{%
supscrip.wmf}{\special{language "Scientific Word";type "GRAPHIC";display
"PICT";valid_file "F";width 19.5625pt;height 18.8125pt;depth
2pt;original-width 17.8125pt;original-height 16.9375pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'supscrip.wmf';file-properties
"XNPEU";}}, type \textbf{2},\textbf{\ }and press spacebar.

\item  Type \textbf{-2=0}.

\item  From the Maple menu, choose Solve and then choose Numeric. Maple
returns this numeric solution: \medskip 
\[
\fbox{%
\begin{tabular}{lllll}
\rule[-0.1in]{0in}{0.3in} &  & $x^{2}-2=0$, Solution is : $\left\{
x=-1.\,4142\right\} ,\allowbreak \left\{ x=1.\,4142\right\} $ & 
\rule[-0.1in]{0in}{0.3in} & 
\end{tabular}
}
\]
\medskip 
\end{enumerate}

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Solve a
system of equations}

\begin{enumerate}
\item  From the Insert menu, choose Matrix and specify 2 rows and 1 column.

\item  Choose OK.

\item  Type \textbf{2x+3y=41 }and press Tab.

\item  Type \textbf{x+y=146 }and press spacebar. On your screen, you see
this matrix: $
\begin{array}{l}
2x+3y=41 \\ 
x+y=146
\end{array}
$

\item  Click\FRAME{itbpF}{21.0625pt}{21.0625pt}{2pt}{}{}{solve.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 21.0625pt;height 21.0625pt;depth
2pt;original-width 18.8125pt;original-height 18.8125pt;cropleft "0";croptop
"1.0079";cropright "1.0079";cropbottom "0";filename
'solve.wmf';file-properties "XNPEU";}}or, from the Maple menu, choose Solve
and then choose Exact. Maple solves the system of equations in the matrix
and displays this result: \ \medskip 
\[
\fbox{%
\begin{tabular}{lllll}
\rule[-0.2in]{0in}{0.5in} &  & $
\begin{array}{l}
2x+3y=41 \\ 
x+y=146
\end{array}
$, Solution is : $\left\{ y=-251,x=397\right\} $ & \rule[-0.2in]{0in}{0.5in}
& 
\end{tabular}
}
\]
\medskip \medskip 
\end{enumerate}

\subparagraph{Solve these expressions\textit{\label{exercises}}}

\begin{quotation}
\noindent \qquad Use Solve Exact to solve these relations:\medskip

\[
\dfrac{1}{x}+\dfrac{1}{y}=1(\text{Solve for }x)\text{\hspace{0.5in}}%
x^{2}-5x+4=0\text{\hspace{0.5in}}\dfrac{7-2x}{x-2}\geq 0\text{\hspace{0.5in}}%
\left[ 
\begin{array}{l}
2x+y=5 \\ 
3x-7y=2
\end{array}
\right] 
\]

$\medskip $

\noindent \qquad Use Solve Numeric to solve these relations:\medskip

\[
16-7y=10y-4\text{\hspace{0.5in}}x^{5}-5x^{4}+3x+4=0\text{\hspace{0.5in}}%
\left[ 
\begin{array}{l}
\sin x=\cos x \\ 
x\in \left( 9,12\right)
\end{array}
\right] 
\]
\end{quotation}

\end{document}
