$$x+\frac{1}{x}=81; x^{2}+\frac{1}{x^{2}}=$$
$x=\frac{81-\sqrt{6557}}{2}\approx 0.012347561\text{, }y=6559$
$x=\frac{\sqrt{6557}+81}{2}\approx 80.987652439\text{, }y=6559$
