Let $x$ and $y$ be two rational numbers such that $$x^5 + y^5 = 2x^2y^2.$$Prove that $\sqrt{1-xy}$ is also a rational number.
Source: Malaysia IMONST2 2021 Senior #3
Tags: number theory
Let $x$ and $y$ be two rational numbers such that $$x^5 + y^5 = 2x^2y^2.$$Prove that $\sqrt{1-xy}$ is also a rational number.