Question 193
Suppose $a$, $b$, $c$ are positive numbers such that
$$
(a + b + c) \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right) \lt 5 + 3\sqrt{2} .
$$
Prove that $a$, $b$, $c$ are the side lengths of an acute-angled triangle.
$$
(a + b + c) \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right) \lt 5 + 3\sqrt{2} .
$$
Prove that $a$, $b$, $c$ are the side lengths of an acute-angled triangle.