Another System
Source: HMMT 2008 Guts Problem 33
May 13, 2008
Problem Statement
Let , , be nonzero real numbers such that a\plus{}b\plus{}c\equal{}0 and a^3\plus{}b^3\plus{}c^3\equal{}a^5\plus{}b^5\plus{}c^5. Find the value of
a^2\plus{}b^2\plus{}c^2.