Inegalitate conditionata
Posted: Mon Feb 02, 2009 11:09 pm
Fie \( a,b,c\in \mathbb{R}^*_+ \) astfel incat \( a^2+b^2+c^2=3 \) . Sa se arate ca \( (\forall)x,y,z\in \mathbb{R}_+^* \) avem :
\( \frac{x}{a}+\frac{y}{b}+\frac{z}{c}\ge \sqrt{xy}+\sqrt{yz}+\sqrt{zx} \)
Marius Damian
\( \frac{x}{a}+\frac{y}{b}+\frac{z}{c}\ge \sqrt{xy}+\sqrt{yz}+\sqrt{zx} \)
Marius Damian