Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$ I am having trouble with this problem from my latest homework.
Prove the arithmetic-geometric mean inequality. That is, for two positive real
numbers $x,y$, we have
$$ \sqrt{xy}≤ \frac{x+y}{2} .$$
Furthermore, equality occurs if and only if $x = y$.
Any and all help would be appreciated.

Since $x$ and $y$ are positive, we can write them as $x=u^2$, $y=v^2$. Then
$$(u-v)^2 \geq 0 \Rightarrow u^2 + v^2 \geq 2uv$$
which is precisely it.
