$$\left. \begin{array} { l } { x ^ { 2 } + \frac { 1 } { x ^ { 2 } } = 18 } \\ { x ^ { 3 } - \frac { 1 } { x ^ { 3 } } } \end{array} \right.$$
$x=\sqrt{5}-2\approx 0.236067977\text{, }y=-76$
$x=2-\sqrt{5}\approx -0.236067977\text{, }y=76$
$x=\sqrt{5}+2\approx 4.236067977\text{, }y=76$
$x=-\left(\sqrt{5}+2\right)\approx -4.236067977\text{, }y=-76$
$x=2-\sqrt{5}\approx -0.236067977\text{, }y=76$
$x=\sqrt{5}-2\approx 0.236067977\text{, }y=-76$
$x=-\sqrt{5}-2\approx -4.236067977\text{, }y=-76$
$x=\sqrt{5}+2\approx 4.236067977\text{, }y=76$
