Y by Adventure10 and 1 other user
Let
be real numbers. Prove that
![\[ \frac 1{a(1+b)}+\frac 1{b(1+c)}+\frac 1{c(1+a)}\geq \frac 3{ 1+abc}. \]](//latex.artofproblemsolving.com/0/9/f/09fee86fb6ae5286ff38443f1590d912c4831d80.png)
Greece
EDIT BY DARIJ:
Please use this topic to discuss the sources and history of the above inequality,
and use http://www.mathlinks.ro/Forum/viewtopic.php?t=161059 to discuss the inequality itself (i. e. different proofs and generalizations).

![\[ \frac 1{a(1+b)}+\frac 1{b(1+c)}+\frac 1{c(1+a)}\geq \frac 3{ 1+abc}. \]](http://latex.artofproblemsolving.com/0/9/f/09fee86fb6ae5286ff38443f1590d912c4831d80.png)
Greece
EDIT BY DARIJ:
Please use this topic to discuss the sources and history of the above inequality,
and use http://www.mathlinks.ro/Forum/viewtopic.php?t=161059 to discuss the inequality itself (i. e. different proofs and generalizations).
This post has been edited 1 time. Last edited by Valentin Vornicu, May 3, 2006, 3:18 PM