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a,b,c,x,y,z in inequality

Source: Indonesia IMO 2010 TST, Stage 1, Test 1, Problem 1

November 12, 2009
inequalitiesinequalities proposed

Problem Statement

Let a a, b b, and c c be non-negative real numbers and let x x, y y, and z z be positive real numbers such that a\plus{}b\plus{}c\equal{}x\plus{}y\plus{}z. Prove that \dfrac{a^3}{x^2}\plus{}\dfrac{b^3}{y^2}\plus{}\dfrac{c^3}{z^2} \ge a\plus{}b\plus{}c. Hery Susanto, Malang
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