# Question on GP/APs

1. Jan 8, 2004

### 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.

2. Jan 8, 2004

### 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