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Old Inequality on Iran NMO

Source: Iran National Olympiad - 2014 Second Round - D1P3

May 1, 2014
inequalitiesquadraticsfunctionalgebraquadratic formulainequalities unsolved

Problem Statement

Let x,y,z x,y,z be three non-negative real numbers such that x2+y2+z2=2(xy+yz+zx).x^2+y^2+z^2=2(xy+yz+zx). Prove that x+y+z3≥2xyz3.\dfrac{x+y+z}{3} \ge \sqrt[3]{2xyz}.
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