Question 5
Given that $a$, $b$ and $c$ are positive real numbers such that $ab + bc + ca \ge 1$, prove that
$$
\frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2} \ge \frac{\sqrt{3}}{abc}.
$$
$$
\frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2} \ge \frac{\sqrt{3}}{abc}.
$$