KZ-MO 2004 Problem 7

Prove that for any $a>0,b>0,c>0$ we have $8a^2 b^2 c^2 \geq (a^2 + ab + ac - bc)(b^2 + ba + bc - ac)(c^2 + ca + cb - ab)$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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