Prove that for all rational number $a$ and $b$, $\frac{a+b}{2}$ ≥ $\sqrt{ab}$

Question

Prove that for all rational numbers (can be integer) a y b, $\frac{a+b}{2}$ ≥ $\sqrt{ab}$

Answer 1

Hint:

$$(a+b)^2\ge4ab\iff (a-b)^2\ge0$$

It is important $\;a,b\;$ non-negative ...

Answer 2

by squaring and rearranging we get $$(a-b)^2\geq 0$$ which is true.