Question 167
Prove that if $a$, $b$, $c$ are the lengths of the sides of a triangle, then
$$
\sqrt{\frac{a}{-a+b+c}} + \sqrt{\frac{b}{a-b+c}} + \sqrt{\frac{c}{a+b-c}} \ge 3.
$$
$$
\sqrt{\frac{a}{-a+b+c}} + \sqrt{\frac{b}{a-b+c}} + \sqrt{\frac{c}{a+b-c}} \ge 3.
$$