Question 75
For any positive real numbers $a$, $b$, $c$ satisfying $a + b + c = 1$, prove that
$$
\sqrt{a^2 - 2bc + 2c} + \sqrt{b^2 - 2ca + 2a} + \sqrt{c^2 - 2ab + 2b} \ge \sqrt{5}.
$$
$$
\sqrt{a^2 - 2bc + 2c} + \sqrt{b^2 - 2ca + 2a} + \sqrt{c^2 - 2ab + 2b} \ge \sqrt{5}.
$$