Let a and b be positive real numbers. Prove that

(a+2)(b+2)(a+b)>16ab

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- Jun 24th 2009, 04:27 AMthe undertakeralgebra problem
Let a and b be positive real numbers. Prove that

(a+2)(b+2)(a+b)__>__16ab - Jun 24th 2009, 04:40 AMTheAbstractionist
By AM–GM,

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

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

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

The result follows.