A simple but nice inequality

Agr_94_Math · Yang-Mills Theory Offline Joined: 17 Feb 2008 Posts: 714

Given real numbers $a,b,c$ such that $\frac {1}{2} \le a,b,c \le 1$
Prove that $2\le \sum \frac {a + b}{1 + c} \le 3$ .

**Posted:** Sun Nov 08, 2009 12:12 am

Pain rinnegan · Poincare Conjecture Offline Joined: 16 Apr 2009 Posts: 176

**Posted:** Sun Nov 08, 2009 12:46 am

aadil

$\frac {a + b}{1 + c} < = \frac {2(a + b)}{3}, \frac {b + c}{1 + a} < = \frac {2(b + c)}{3}, \frac {a + c}{1 + b} < =...$ .on adding we get $\sum_cyc \frac {a + b}{1 - c} < = \frac {4(a + b + c)}{3} < = 3.$
i am unable to prove the left hand side Sad

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http://www.artofproblemsolving.com/Forum/viewtopic.php?t=84221
also,

**Posted:** Sun Nov 08, 2009 3:58 am

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