mateforum.ro
MateForum
http://www.mateforum.ro/
Inegalitate simpla
http://www.mateforum.ro/viewtopic.php?t=4364
Page
1
of
1
Inegalitate simpla
Posted:
Mon Jul 13, 2009 2:40 am
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
Posted:
Mon Jul 13, 2009 11:17 am
by
Marius Mainea
\( LHS\le\sum \frac{ab}{2ab+\sqrt{c}}=\sum\frac{1}{2+c\sqrt{c}}=\sum\frac{1}{2+\frac{x}{y}}\le RHS \)