Hii !
Let x,y and z be Positive real numbers . prove That :
$\displaystyle \frac{(x+y+z)^3}{xyz} \geq 27(\frac{x+y}{x+z}+\frac{x+z}{x+y}-1)$
You should be posting under the Math Challenge Problems section. This section is meant to help those with their homework problems (and not to supply an answer which is what you're looking for when you're asking for a proof). Also your problems are too advanced for this section (btw - I like your problems).