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Decrementing the power

Source: Indonesian Mathematics Olympiad 2011, Day 2, Problem 7

September 14, 2011

inequalities proposedinequalities

Problem Statement

Let

a,b,c \in \mathbb{R}^+

and

abc = 1

such that

a^{2011} + b^{2011} + c^{2011} < \dfrac{1}{a^{2011}} + \dfrac{1}{b^{2011}} + \dfrac{1}{c^{2011}}

. Prove that

a + b + c < \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c}