Inegalitate simpla

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opincariumihai
Thales
Posts: 134
Joined: Sat May 09, 2009 7:45 pm
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Inegalitate simpla

Post by opincariumihai »

Daca \( a,b,c \) sunt pozitive si \( abc=1 \) aratati ca \( \sum\frac{ab}{a^2+b^2+\sqrt{c}}\leq1 \)

Mihai Opincariu
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Marius Mainea
Gauss
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Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Post by Marius Mainea »

\( LHS\le\sum \frac{ab}{2ab+\sqrt{c}}=\sum\frac{1}{2+c\sqrt{c}}=\sum\frac{1}{2+\frac{x}{y}}\le RHS \)
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