$$x+\frac{1}{x}=79; x^{2}+\frac{1}{x^{2}}=$$
$x=\frac{79-9\sqrt{77}}{2}\approx 0.012660257\text{, }y=6239$
$x=\frac{9\sqrt{77}+79}{2}\approx 78.987339743\text{, }y=6239$
