$${ x }^{ 2 } + \frac{ 1 }{ { x }^{ 2 } } =18, { x }^{ 3 } + \frac{ 1 }{ { x }^{ 3 } } =$$
$x=\sqrt{5}-2\approx 0.236067977\text{, }y=34\sqrt{5}\approx 76.026311235$
$x=2-\sqrt{5}\approx -0.236067977\text{, }y=-34\sqrt{5}\approx -76.026311235$
$x=\sqrt{5}+2\approx 4.236067977\text{, }y=34\sqrt{5}\approx 76.026311235$
$x=-\left(\sqrt{5}+2\right)\approx -4.236067977\text{, }y=-34\sqrt{5}\approx -76.026311235$
$x=2-\sqrt{5}\approx -0.236067977\text{, }y=-34\sqrt{5}\approx -76.026311235$
$x=\sqrt{5}-2\approx 0.236067977\text{, }y=34\sqrt{5}\approx 76.026311235$
$x=-\sqrt{5}-2\approx -4.236067977\text{, }y=-34\sqrt{5}\approx -76.026311235$
$x=\sqrt{5}+2\approx 4.236067977\text{, }y=34\sqrt{5}\approx 76.026311235$
