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Polynomial inequality in three variables

Source: Austrian Math Olympiad 2016, final round, problem 4

May 26, 2016
algebrapolynomialinequalities

Problem Statement

Let a,b,c≥−1a,b,c\ge-1 be real numbers with a3+b3+c3=1a^3+b^3+c^3=1. Prove that a+b+c+a2+b2+c2≤4a+b+c+a^2+b^2+c^2\le4, and determine the cases of equality.
(Proposed by Karl Czakler)
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