MathDB
Sorry for this one: (a^2+2b^2)/(b+c) + ... >= 3/2 (a+b+c)

Source: 3rd QEDMO 2006, problem 11, by me

April 14, 2006
inequalities

Problem Statement

Guess I should stop proposing problems at 2:00 AM, as this can lead to ones like this here: Let aa, bb, cc be three positive reals. Prove the inequality a2+2b2b+c+b2+2c2c+a+c2+2a2a+b≥32(a+b+c)\frac{a^2+2b^2}{b+c}+\frac{b^2+2c^2}{c+a}+\frac{c^2+2a^2}{a+b}\geq\frac32\left(a+b+c\right).
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