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Symmetric inequality FTW

Source: Latvian TST for Baltic Way 2020 P1

October 17, 2020
inequalitiesSymmetric inequalityFTWalgebraHi

Problem Statement

Prove that for positive reals a,b,ca,b,c satisfying a+b+c=3a+b+c=3 the following inequality holds: a1+2b3+b1+2c3+c1+2a3≥1 \frac{a}{1+2b^3}+\frac{b}{1+2c^3}+\frac{c}{1+2a^3} \ge 1
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