Inegalitate de Dan Marinache

Moderators: Laurian Filip, Beniamin Bogosel, Filip Chindea

Post Reply
alex2008
Leibniz
Posts: 464
Joined: Sun Oct 19, 2008 3:23 pm
Location: Tulcea

Inegalitate de Dan Marinache

Post by alex2008 »

Daca \( a,b,c >0 \) astfel incat \( abc=1 \), sa se demonstreze ca :

\( \frac{2a}{ab+1}+\frac{2b}{bc+1}+\frac{2c}{ca+1}\le a\sqrt{c}+b\sqrt{a}+c\sqrt{b} \)

Dan Marinache
. A snake that slithers on the ground can only dream of flying through the air.
Top
Marius Mainea
Gauss
Posts: 1077
Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Post by Marius Mainea »

Din AM-GM

\( LHS\le \sum {\frac{2a}{2\sqrt{ab}}=\sum {\sqrt{\frac{a}{b}}}=RHS \)
Top
Post Reply

Return to “Clasa a IX-a”