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Bosnia and Herzegovina JBMO TST 2014 Problem 3

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2014

September 16, 2018
algebrainequalities

Problem Statement

Let aa, bb and cc be positive real numbers such that a+b+c=1a+b+c=1. Prove the inequality: 1(a+2b)(b+2a)+1(b+2c)(c+2b)+1(c+2a)(a+2c)≥3\frac{1}{\sqrt{(a+2b)(b+2a)}}+\frac{1}{\sqrt{(b+2c)(c+2b)}}+\frac{1}{\sqrt{(c+2a)(a+2c)}} \geq 3
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