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Nesbitt-like Inequality from Nordic Math Contest 2005

Source: Nordic Mathematical Contest, April 2005

April 11, 2005
inequalitiescalculusinequalities proposedalgebraHigh school olympiad

Problem Statement

Let a,b,ca,b,c be positive real numbers. Prove that 2a2b+c+2b2c+a+2c2a+b≥a+b+c\frac{2a^2}{b+c} + \frac{2b^2}{c+a} + \frac{2c^2}{a+b} \geq a+b+c(this is, of course, a joke!) EDITED with exponent 2 over c
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