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a(b -c)^2 + b(c - a)^2 + c(a - b)^2 + 4abc > a^3 + b^3 + c^3

Source: 1972 Hungary - Kürschák Competition p1

October 15, 2022
geometryGeometric Inequalitiesinequalities

Problem Statement

A triangle has side lengths a,b,ca, b, c. Prove that a(b−c)2+b(c−a)2+c(a−b)2+4abc>a3+b3+c3a(b -c)^2 + b(c - a)^2 + c(a - b)^2 + 4abc > a^3 + b^3 + c^3
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