Question 40
Let $a$, $b$ and $c$ be the side lengths of an arbitrary triangle with perimeter equal to $1$.
Show that
$$
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} \gt \frac{9}{\sqrt{1-a} + \sqrt{1-b} + \sqrt{1-c}}.
$$
Show that
$$
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} \gt \frac{9}{\sqrt{1-a} + \sqrt{1-b} + \sqrt{1-c}}.
$$