Question 18
Let $a$, $b$ and $c$ be positive real numbers. show that
$$
\left(\frac{a}{b+c} + \frac{1}{2}\right) \left(\frac{b}{c+a} + \frac{1}{2}\right) \left(\frac{c}{a+b} + \frac{1}{2}\right) \ge 1
$$
$$
\left(\frac{a}{b+c} + \frac{1}{2}\right) \left(\frac{b}{c+a} + \frac{1}{2}\right) \left(\frac{c}{a+b} + \frac{1}{2}\right) \ge 1
$$