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Bosnia and Herzegovina TST 2000 Day 2 Problem 1

Source: Bosnia and Herzegovina Team Selection Test 2000

September 19, 2018

algebraInequalityinequalities

Problem Statement

Prove that for all positive real

a

b

and

c

holds:

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