Proving inequality with a, b

[x-mather]

Prove that for any positive real numbers a, b this inequality is valid:

 

[Deleted member 4993]

Prove that for any positive real numbers a, b this inequality is valid:

The inequality:

$\displaystyle \sqrt{ab} \le \frac{a+b}{2}$

is quite easy to prove. Start with the fact that:

$\displaystyle (a+b)^2 - (a-b)^2 = 4ab$

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.