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2006 Romanian NMO Problems/Grade 8/Problem 4

Revision as of 23:22, 10 November 2006 by JBL (talk | contribs)

Problem

Let $a,b,c \in \left[ \frac 12, 1 \right]$. Prove that

$2 \leq \frac{ a+b}{1+c} + \frac{ b+c}{1+a} + \frac{ c+a}{1+b} \leq 3$.

selected by Mircea Lascu

Solution

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