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Inegalitate conditionata 3
Posted: Sat Dec 20, 2008 11:30 pm
by Marius Mainea
Fie a,b,c nenegative cu a+b+c=1. Demonstrati ca:
\( \frac{a^2b^2}{1-ab}+\frac{b^2c^2}{1-bc}+\frac{c^2a^2}{1-ca}\le \frac{1}{12}. \)
Posted: Mon Jan 05, 2009 11:04 pm
by Marius Mainea
Avem \( ab\le(\frac{a+b}{2})^2\le (\frac{a+b+c}{2})^2=\frac{1}{4} \) si analoagele deci
\( LHS\le\frac{4}{3}(a^2b^2+b^2c^2+c^2a^2)\le \frac{1}{12} \)(demonstrati)
Posted: Wed Jan 07, 2009 9:01 pm
by Marius Mainea
Marius Mainea wrote:
\( LHS\le\frac{4}{3}(a^2b^2+b^2c^2+c^2a^2)\le \frac{1}{12} \)(demonstrati)
Fie a= max(a,b,c)
\( ab+ac=a(b+c)\le (\frac{a+b+c}{2})^2=\frac{1}{4} \)