HMMT 2008 U33

Let $a, b, c$ be nonzero real numbers such that $a+b+c=0$ and $a^{3}+b^{3}+c^{3}=a^{5}+b^{5}+c^{5}$ . Find the value of $a^{2}+b^{2}+c^{2}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{6}{5}

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