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Regional Olympiad - FBH 2015 Grade 10 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2015

September 23, 2018

inequalitiesalgebra

Problem Statement

Let

a

b

and

c

be positive real numbers such that

abc=1

. Prove the inequality:

\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a} \leq \frac{a^2+b^2+c^2}{2}