ILL 1992 Problem 21

Prove that if $x,y,z >1$ and $\frac 1x +\frac 1y +\frac 1z = 2$ , then $\sqrt{x+y+z} \geq \sqrt{x-1}+\sqrt{y-1}+\sqrt{z-1}.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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