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inequality abc=1

Source: China south east mathematical Olympiad 2007 problem 4

July 12, 2013
inequalitiesinequalities unsolved

Problem Statement

Let aa,bb,cc be positive real numbers satisfying abc=1abc=1. Prove that inequality aka+b+bkb+c+ckc+a≥32\dfrac{a^k}{a+b}+ \dfrac{b^k}{b+c}+\dfrac{c^k}{c+a}\ge \dfrac{3}{2} holds for all integer kk (k≥2k \ge 2).
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