Question 62
Let $a$, $b$, $c$ be positive real numbers such that $ab + bc + ca = 1$. Show that
$$
\sqrt{3}(\sqrt{a} + \sqrt{b} + \sqrt{c}) \le \frac{a\sqrt{a}}{bc} + \frac{b\sqrt{b}}{ca} + \frac{c\sqrt{c}}{ab}.
$$
$$
\sqrt{3}(\sqrt{a} + \sqrt{b} + \sqrt{c}) \le \frac{a\sqrt{a}}{bc} + \frac{b\sqrt{b}}{ca} + \frac{c\sqrt{c}}{ab}.
$$