Question 9
For positive numbers $a, b, c$ prove the inequality :
$$
\sqrt{a^2 + bc} + \sqrt{b^2 + ca} + \sqrt{c^2 + ab} \ge \sqrt{ab + bc} + \sqrt{bc + ca} + \sqrt{ca + ab}.
$$
$$
\sqrt{a^2 + bc} + \sqrt{b^2 + ca} + \sqrt{c^2 + ab} \ge \sqrt{ab + bc} + \sqrt{bc + ca} + \sqrt{ca + ab}.
$$