Question 6
Let $a$, $b$ and $c$ be positive real numbers. show that
$$
\frac{a+b}{c^2} + \frac{c+a}{b^2} + \frac{b+c}{a^2} \ge \frac{9}{a+b+c} + \frac{1}{a} + \frac{1}{b} + \frac{1}{c}
$$
$$
\frac{a+b}{c^2} + \frac{c+a}{b^2} + \frac{b+c}{a^2} \ge \frac{9}{a+b+c} + \frac{1}{a} + \frac{1}{b} + \frac{1}{c}
$$