$$x + \frac { 1 } { x } = 2 \sqrt { 2 } , x \gt 0 , x \gt 0 , x - \frac { 1 } { x }$$
$\left\{\begin{matrix}x=\sqrt{2}-1\text{, }&y=-2\\x=\sqrt{2}+1\text{, }&y=2\end{matrix}\right.$
$\left\{\begin{matrix}y=-2\text{, }&x=\sqrt{2}-1\\y=2\text{, }&x=\sqrt{2}+1\end{matrix}\right.$
