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Difference between revisions of "2006 Romanian NMO Problems/Grade 8/Problem 4"

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==See also==
 
==See also==
 
*[[2006 Romanian NMO Problems/Grade 8/Problem 3 | Previous problem]]
 
*[[2006 Romanian NMO Problems/Grade 8/Problem 3 | Previous problem]]
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*[[2006 Romanian NMO Problems/Grade 8/Problem 5 | Next problem]]
 
 
*[[2006 Romanian NMO Problems]]
 
*[[2006 Romanian NMO Problems]]
 
[[Category:Olympiad Algebra Problems]]
 
[[Category:Olympiad Algebra Problems]]

Revision as of 23:22, 10 November 2006

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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See also

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