Question 84
Let $a, b, c \in (0, \infty)$. Prove the inequality
$$
\frac{a - \sqrt{bc}}{a + 2(b + c)} + \frac{b - \sqrt{ca}}{b + 2(c + a)} + \frac{c - \sqrt{ab}}{c + 2(a + b)} \geq 0.
$$
$$
\frac{a - \sqrt{bc}}{a + 2(b + c)} + \frac{b - \sqrt{ca}}{b + 2(c + a)} + \frac{c - \sqrt{ab}}{c + 2(a + b)} \geq 0.
$$