MathNet 2008-part-05 — 164 problems (EN–VI) Question 51

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 $a^{2}+b^{2}+c^{2}$.