Problem #PRU-110047

Problem

We call a number $x$ rational if it can be represented as $x=\frac{p}{q}$ for coprime integers $p$ and $q$. Otherwise we call the number irrational.
Non-zero numbers $a$ and $b$ satisfy the equality $a^2{b}^2(a^2{b}^2+4)=2(a^6+b^6)$. Prove that at least one of them is irrational.