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\sqrt{a^3b+a^3c}+\sqrt{b^3c+b^3a}+\sqrt{c^3a+c^3b}\ge 4/3 (ab+bc+ca)

Source: Balkan BMO Shortlist 2016 A1

July 30, 2019
inequalitiesthree variable inequalityalgebraIMO Shortlist

Problem Statement

Let a,b,ca, b,c be positive real numbers. Prove that a3b+a3c+b3c+b3a+c3a+c3b≥43(ab+bc+ca) \sqrt{a^3b+a^3c}+\sqrt{b^3c+b^3a}+\sqrt{c^3a+c^3b}\ge \frac43 (ab+bc+ca)
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