$$(x^{2}+\frac{1}{x^{2}})-(x-\frac{1}{x})-4=0$$
$x=\sqrt{2}+1\approx 2.414213562$
$x=1-\sqrt{2}\approx -0.414213562$
$x=\frac{-\sqrt{5}-1}{2}\approx -1.618033989$
$x=\frac{\sqrt{5}-1}{2}\approx 0.618033989$
