Q:

# Solve geographically and graphically x+y=6 Xy=2

Accepted Solution

A:
$\left\{\begin{array} { l } x+y=6 \\ xy=2\end{array} \right.$
$\left\{\begin{array} { l } x=6-y \\ xy=2\end{array} \right.$
$\left( 6-y \right)y=2$
$\begin{array} { l }y=3+\sqrt{ 7 },\\y=3-\sqrt{ 7 }\end{array}$
$\begin{array} { l }x=6-\left( 3+\sqrt{ 7 } \right),\\y=3-\sqrt{ 7 }\end{array}$
$\begin{array} { l }x=6-\left( 3+\sqrt{ 7 } \right),\\x=6-\left( 3-\sqrt{ 7 } \right)\end{array}$
$\begin{array} { l }x=3-\sqrt{ 7 },\\x=6-\left( 3-\sqrt{ 7 } \right)\end{array}$
$\begin{array} { l }x=3-\sqrt{ 7 },\\x=3+\sqrt{ 7 }\end{array}$
$\begin{array} { l }\left( x_1, y_1\right)=\left( 3-\sqrt{ 7 }, 3+\sqrt{ 7 }\right),\\\left( x_2, y_2\right)=\left( 3+\sqrt{ 7 }, 3-\sqrt{ 7 }\right)\end{array}$
$\begin{array} { l }\left\{\begin{array} { l } 3-\sqrt{ 7 }+3+\sqrt{ 7 }=6 \\ \left( 3-\sqrt{ 7 } \right) \times \left( 3+\sqrt{ 7 } \right)=2\end{array} \right.,\\\left\{\begin{array} { l } 3+\sqrt{ 7 }+3-\sqrt{ 7 }=6 \\ \left( 3+\sqrt{ 7 } \right) \times \left( 3-\sqrt{ 7 } \right)=2\end{array} \right.\end{array}$
$\begin{array} { l }\left\{\begin{array} { l } 6=6 \\ 2=2\end{array} \right.,\\\left\{\begin{array} { l } 3+\sqrt{ 7 }+3-\sqrt{ 7 }=6 \\ \left( 3+\sqrt{ 7 } \right) \times \left( 3-\sqrt{ 7 } \right)=2\end{array} \right.\end{array}$
$\begin{array} { l }\left\{\begin{array} { l } 6=6 \\ 2=2\end{array} \right.,\\\left\{\begin{array} { l } 6=6 \\ 2=2\end{array} \right.\end{array}$
$\begin{array} { l }\left( x_1, y_1\right)=\left( 3-\sqrt{ 7 }, 3+\sqrt{ 7 }\right),\\\left( x_2, y_2\right)=\left( 3+\sqrt{ 7 }, 3-\sqrt{ 7 }\right)\end{array}$