Question 31
Find all real $p$ such that the inequality
$$
\sqrt{a^2 + p b^2} + \sqrt{b^2 + p a^2} \ge a + b + (p-1)\sqrt{ab}
$$
holds for any real $a$ and $b$.
$$
\sqrt{a^2 + p b^2} + \sqrt{b^2 + p a^2} \ge a + b + (p-1)\sqrt{ab}
$$
holds for any real $a$ and $b$.