$$x+\frac{1}{x^{2}}=12; x^{4}-\frac{1}{x^{4}}=?$$
$x=\frac{\sqrt{10}-\sqrt{14}}{2}\approx -0.289689863\text{, }y=-24\sqrt{35}\approx -141.985914794$
$x=\frac{\sqrt{14}-\sqrt{10}}{2}\approx 0.289689863\text{, }y=-24\sqrt{35}\approx -141.985914794$
$x=\frac{-\sqrt{10}-\sqrt{14}}{2}\approx -3.451967523\text{, }y=24\sqrt{35}\approx 141.985914794$
$x=\frac{\sqrt{10}+\sqrt{14}}{2}\approx 3.451967523\text{, }y=24\sqrt{35}\approx 141.985914794$
