$$x+\frac{1}{x}=3; x^{5}+\frac{1}{x^{5}}=?$$
$x=\frac{3-\sqrt{5}}{2}\approx 0.381966011\text{, }y=123$
$x=\frac{\sqrt{5}+3}{2}\approx 2.618033989\text{, }y=123$
