Inequality of arithmetic and geometric mean I did a proof for inequality below, anyone has a other proof?
Let $a$ and $b$ be positive real numbers, and $t$ the parameter. Prove that:
$$a+b\geq 2\sqrt{1-t^2}\sqrt{ab}+(a-b)t$$

Your inequality is wrong! Try $t=2$.
For $-1\leq t\leq 1$ we need to prove that
$$(1-t)a+(1+t)b\geq2\sqrt{(1-t)(1+t)ab},$$
which is just AM-GM
