CMR :
$\frac{ab}{c+1} + \frac{bc}{a+1} + \frac{ac}{b+1} \leqslant \frac{1}{4}$
Chứng minh bất đẳng thức với a,b,c 0 và a+b+c =1
Started By mango, 30-03-2012 - 12:34
#2
Posted 30-03-2012 - 17:14
phantomladyvskaitokid
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CMR :
$\frac{ab}{c+1} + \frac{bc}{a+1} + \frac{ac}{b+1} \leqslant \frac{1}{4}$
$\frac{ab}{c+1}+\frac{bc}{a+1}+\frac{ca}{b+1}$
$=\frac{ab}{a+b+2c}+\frac{bc}{b+c+2a}+\frac{ca}{c+a+2b}$
$\leq \frac{1}{4}(\frac{ab}{a+c}+\frac{ab}{b+c}+\frac{bc}{b+a}+\frac{bc}{a+c}+\frac{ca}{c+b}+\frac{ca}{b+c})$
$= \frac{1}{4}(a+b+c)$
$= \frac{1}{4}$
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