Non-zero numbers $a$ and $b$ satisfy the equality $$a^2b^2(a^2b^2 + 4) = 2(a^6 + b^6).$$Prove that at least one of them is irrational.
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Tags: algebra, irrational
Non-zero numbers $a$ and $b$ satisfy the equality $$a^2b^2(a^2b^2 + 4) = 2(a^6 + b^6).$$Prove that at least one of them is irrational.