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\sqrt {x-1}+...

Source: Iran Third Round MO 1997, Exam 3, P4

October 18, 2005
inequalitiesCauchy Inequalityinequalities proposed

Problem Statement

Let x,y,zx, y, z be real numbers greater than 11 such that 1x+1y+1z=2\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=2. Prove that x−1+y−1+z−1≤x+y+z.\sqrt{x-1}+\sqrt{y-1}+\sqrt{z-1}\leq \sqrt{x+y+z}.
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