$$x + \frac { 1 } { x } = 5 , x ^ { 4 } + \frac { 1 } { x ^ { 4 } }$$
$x=\frac{5-\sqrt{21}}{2}\approx 0.208712153\text{, }y=527$
$x=\frac{\sqrt{21}+5}{2}\approx 4.791287847\text{, }y=527$
