Question 42
For any positive real numbers $a$, $b$, $c$, prove that
$$
(ab + bc + ca) \left( \frac{1}{(a+b)^2} + \frac{1}{(b+c)^2} + \frac{1}{(c+a)^2} \right) \ge \frac{9}{4}.
$$
$$
(ab + bc + ca) \left( \frac{1}{(a+b)^2} + \frac{1}{(b+c)^2} + \frac{1}{(c+a)^2} \right) \ge \frac{9}{4}.
$$