MathDB
Inequality

Source: 2013 Baltic Way, Problem 4

December 30, 2013
inequalitiesfunctionrearrangement inequalityinequalities unsolved

Problem Statement

Prove that the following inequality holds for all positive real numbers x,y,zx,y,z: x3y2+z2+y3z2+x2+z3x2+y2≥x+y+z2.\dfrac{x^3}{y^2+z^2}+\dfrac{y^3}{z^2+x^2}+\dfrac{z^3}{x^2+y^2}\ge \dfrac{x+y+z}{2}.
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