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Found problems: 1

2006 Junior Balkan Team Selection Tests - Romania, 3
Tags: algebra , ss , inequalities
Let $a,b,c>0$ be real numbers with sum 1. Prove that \[ \frac{a^2}b + \frac{b^2}c + \frac{c^2} a \geq 3(a^2+b^2+c^2) . \]