AUSTRIAN-POLISH 1991 Problem 5

If $x,y, z$ are arbitrary positive numbers with $xyz = 1$ , prove the inequality $x^2+y^2+z^2 + xy+yz + zx \ge 2(\sqrt{x} +\sqrt{y}+ \sqrt{z})$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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