Explain why for any two positive real numbers x and y, (the geometric mean is always less than the arithmetic mean.)

Squaring each side gives us,


Multiply by 4,


and subtract,


Expand out the square,


Combine like-terms,


This can now be written as a different perfect square,


Recall that a squared value is always positive. So (x-y)^2 is always greater than zero.

That should "explain it" sufficiently unless you need to do some sort of formal proof.

Hello!
your answer should be c