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Regional Olympiad - FBH 2015 Grade 9 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2015

September 23, 2018
algebraInequality

Problem Statement

Let aa, bb and cc be positive real numbers such that abc=2015abc=2015. Prove that a+ba2+b2+b+cb2+c2+c+ac2+a2≤a+b+c2015\frac{a+b}{a^2+b^2}+\frac{b+c}{b^2+c^2}+\frac{c+a}{c^2+a^2} \leq \frac{\sqrt{a}+\sqrt{b}+\sqrt{c}}{\sqrt{2015}}
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