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Three positive variables with product 1

Source: Tuymaada 2013, Day 1, Problem 4 Seniors

July 24, 2013
inequalitiesTuymaadathree variable inequality

Problem Statement

Prove that if xx, yy, zz are positive real numbers and xyz=1xyz = 1 then x3x2+y+y3y2+z+z3z2+x≥32.\frac{x^3}{x^2+y}+\frac{y^3}{y^2+z}+\frac{z^3}{z^2+x}\geq \dfrac {3} {2}.
A. Golovanov
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