MathDB
a/(2b+c^2) cyclic sum is at most (a^2+b^2+c^2)/3

Source: MEMO 2015, problem T-1

August 28, 2015
inequalitiesFractionmuirhed inequality

Problem Statement

Prove that for all positive real numbers aa, bb, cc such that abc=1abc=1 the following inequality holds: a2b+c2+b2c+a2+c2a+b2≤a2+b2+c23.\frac{a}{2b+c^2}+\frac{b}{2c+a^2}+\frac{c}{2a+b^2}\le \frac{a^2+b^2+c^2}3.
Back to ProblemsView on AoPS