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Problem 8 of Russian Regional Olympiad 2011, grade 11

Source: Problem 8 of Russian Regional Olympiad 2011, grade 11

September 1, 2011
inequalitiesinequalities proposed

Problem Statement

bb and cc are positive. Prove the inequality (b−c)2011(b+c)2011(c−b)2011≥(b2011−c2011)(b2011+c2011)(c2011−b2011). \left(b-c\right)^{2011}\left(b+c\right)^{2011}\left(c-b\right)^{2011} \geq \left(b^{2011}-c^{2011}\right)\left(b^{2011}+c^{2011}\right)\left(c^{2011}-b^{2011}\right). (Author: V. Senderov)
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