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\sum_{cyc} (a^3-b^3)^2+3\sum_{cyc}(a^2-b^2)^2+6(a-b)(b-c)(c-a)(ab+ bc+ca) >= 0.

Source: Mathcenter Contest / Oly - Thai Forum 2011 (R1) p1 sl-1 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 14, 2022
inequalitiesalgebra

Problem Statement

Let a,b,c∈Ra,b,c \in \mathbb{R}. Prove that ∑cyc(a3−b3)2+3∑cyc(a2−b2)2+6(a−b)(b−c)(c−a)(ab+bc+ca)≥0.\sum_{cyc} (a^3-b^3)^2+3\sum_{cyc}(a^2-b^2)^2+6(a-b)(b-c)(c-a)(ab+ bc+ca) \ge 0.
(LightLucifer)
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