Question 5
Let $a,b,c$ be the side lengths of a triangle. Prove that
$$\sqrt{a+b-c}+\sqrt{b+c-a}+\sqrt{c+a-b}\le\sqrt a+\sqrt b+\sqrt c,$$
and determine when equality holds.
$$\sqrt{a+b-c}+\sqrt{b+c-a}+\sqrt{c+a-b}\le\sqrt a+\sqrt b+\sqrt c,$$
and determine when equality holds.