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Inequality

Source: Greece National Olympiad 2002 , Seniors , Problem 1.

November 18, 2005
inequalitiesquadraticsanalytic geometryinequalities proposed

Problem Statement

The real numbers a,b,ca,b,c with bc≠0bc\neq0 satisfy 1−c2bc≥0.\frac{1-c^2}{bc}\geq0. Prove that 10(a2+b2+c2−bc3)≥2ab+5ac.10(a^2+b^2+c^2-bc^3)\geq2ab+5ac.
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