Question 66
Let $a$, $b$ and $c$ be the lengths of sides of a triangle. Prove that
$$
\left| \sqrt{\frac{a}{b}} - \sqrt{\frac{b}{a}} + \sqrt{\frac{b}{c}} - \sqrt{\frac{c}{b}} + \sqrt{\frac{c}{a}} - \sqrt{\frac{a}{c}} \right| \lt \frac{1}{10}.
$$
$$
\left| \sqrt{\frac{a}{b}} - \sqrt{\frac{b}{a}} + \sqrt{\frac{b}{c}} - \sqrt{\frac{c}{b}} + \sqrt{\frac{c}{a}} - \sqrt{\frac{a}{c}} \right| \lt \frac{1}{10}.
$$