ILL 1990 Problem 77

Let $a, b, c \in \mathbb R$ . Prove that $(a^2 + ab + b^2)(b^2 + bc + c^2)(c^2 + ca + a^2) \geq (ab + bc + ca)^3.$ When does the equality hold?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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