# algebra problem

• June 24th 2009, 05:27 AM
the undertaker
algebra problem
Let a and b be positive real numbers. Prove that

(a+2)(b+2)(a+b) > 16ab
• June 24th 2009, 05:40 AM
TheAbstractionist
By AM–GM,

$a+2\ \ge\ 2\sqrt{2a}$

$b+2\ \ge\ 2\sqrt{2b}$

$a+b\ \ge\ 2\sqrt{ab}$

The result follows.