$$x ^ { 2 } + \frac { 1 } { x ^ { 2 } } = 66 , x - \frac { 1 } { x } = t 8$$
$x=\sqrt{17}-4\approx 0.123105626\text{, }t_{8}=-8$
$x=4-\sqrt{17}\approx -0.123105626\text{, }t_{8}=8$
$x=\sqrt{17}+4\approx 8.123105626\text{, }t_{8}=8$
$x=-\left(\sqrt{17}+4\right)\approx -8.123105626\text{, }t_{8}=-8$
$x=4-\sqrt{17}\approx -0.123105626\text{, }t_{8}=8$
$x=\sqrt{17}-4\approx 0.123105626\text{, }t_{8}=-8$
$x=-\sqrt{17}-4\approx -8.123105626\text{, }t_{8}=-8$
$x=\sqrt{17}+4\approx 8.123105626\text{, }t_{8}=8$
