Question 65
Let $a$, $b$ be non-negative real numbers. Prove the inequality
$$
\frac{a}{\sqrt{b^2+1}} + \frac{b}{\sqrt{a^2+1}} \ge \frac{a+b}{\sqrt{ab+1}}
$$
and find when the equality holds.
$$
\frac{a}{\sqrt{b^2+1}} + \frac{b}{\sqrt{a^2+1}} \ge \frac{a+b}{\sqrt{ab+1}}
$$
and find when the equality holds.