Question 26
Let $a$ and $b$ be the legs, and $c$ the hypotenuse of a right triangle.
Prove that the following inequality holds
$$
\left(1 + \frac{c}{a}\right) \left(1 + \frac{c}{b}\right) \geqslant 3 + 2\sqrt{2}.
$$
Prove that the following inequality holds
$$
\left(1 + \frac{c}{a}\right) \left(1 + \frac{c}{b}\right) \geqslant 3 + 2\sqrt{2}.
$$