Question

Let \(x\) and \(y\) be two real numbers with the same sign such that
\(\large y=x+\frac{1}{y+\frac{1}{x+\frac{1}{y}}}\) and \(\large x=y+\frac{1}{x+\frac{1}{y+\frac{1}{x}}}\).
Show that \(x=y\).