$$\left. \begin{array} { l } { x ^ { 2 } + \frac { 1 } { x ^ { 2 } } = 38 } \\ { x + \frac { 1 } { x } } \end{array} \right.$$
$x=\sqrt{10}-3\approx 0.16227766\text{, }y=2\sqrt{10}\approx 6.32455532$
$x=3-\sqrt{10}\approx -0.16227766\text{, }y=-2\sqrt{10}\approx -6.32455532$
$x=\sqrt{10}+3\approx 6.16227766\text{, }y=2\sqrt{10}\approx 6.32455532$
$x=-\left(\sqrt{10}+3\right)\approx -6.16227766\text{, }y=-2\sqrt{10}\approx -6.32455532$
$x=3-\sqrt{10}\approx -0.16227766\text{, }y=-2\sqrt{10}\approx -6.32455532$
$x=\sqrt{10}-3\approx 0.16227766\text{, }y=2\sqrt{10}\approx 6.32455532$
$x=-\sqrt{10}-3\approx -6.16227766\text{, }y=-2\sqrt{10}\approx -6.32455532$
$x=\sqrt{10}+3\approx 6.16227766\text{, }y=2\sqrt{10}\approx 6.32455532$
