$$\left. \begin{array} { l } { x ^ { 2 } + \frac { 1 } { x ^ { 2 } } = 7 } \\ { ( } \\ { x + \frac { 1 } { x } ) } \end{array} \right.$$
$x=\frac{\sqrt{5}-3}{2}\approx -0.381966011\text{, }y=-3$
$x=\frac{3-\sqrt{5}}{2}\approx 0.381966011\text{, }y=3$
$x=\frac{-\sqrt{5}-3}{2}\approx -2.618033989\text{, }y=-3$
$x=\frac{\sqrt{5}+3}{2}\approx 2.618033989\text{, }y=3$
