Prove that there exist infinitely many pairs of real numbers $(x,y)$ such that $\sqrt{1+2x-xy}+\sqrt{1+2y-xy}=2.$
Source: Kyiv mathematical festival 2015
Tags: Kyiv mathematical festival, algebra
Prove that there exist infinitely many pairs of real numbers $(x,y)$ such that $\sqrt{1+2x-xy}+\sqrt{1+2y-xy}=2.$