Question 41
Prove that for all positive real numbers $a$, $b$ and $c$ the following inequality holds
$$
\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b} + \sqrt{\frac{ab+bc+ca}{a^2+b^2+c^2}} \ge \frac{5}{2}.
$$
$$
\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b} + \sqrt{\frac{ab+bc+ca}{a^2+b^2+c^2}} \ge \frac{5}{2}.
$$