GP/APs

[jake_at]

i'm having some trouble with this question on GP/APs. can anybody show me how to do it, and explain? thanks.

:) J.

The Culprit:
Prove that the arithmetic mean of two different positive numbers exceeds the geometric mean of the same two numbers.

[himanshu121]

Let us take two numbers a and b

AM= (a+b)/2 = \frac{(\sqrt{a}-\sqrt{b})^2}{2} + \sqrt{ab}

clearly AM>=GM