TH-TMO 2004 Problem 2

Let $a$ and $b$ be real numbers such that $\begin{cases} a^6 - 3a^2b^4 = 3 b^6 - 3a^4b^2 = 3\sqrt2.\end{cases}$ What is the value of $a^4 + b^4$ ?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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