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An inequality with x+y+z=1

Source: Korea National Olympiad 2010 Problem 5

September 9, 2012
inequalitiestrigonometryAMCUSA(J)MOUSAMOinequalities proposed

Problem Statement

x,y,z x, y, z are positive real numbers such that x+y+z=1 x+y+z=1 . Prove that x1−x+y1−y+z1−z>2 \sqrt{ \frac{x}{1-x} } + \sqrt{ \frac{y}{1-y} } + \sqrt{ \frac{z}{1-z} } > 2
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