Question 173
Let $a_1, a_2, \dots, a_m$ be positive integers, none of which is equal to $10$, such that $a_1 + a_2 + \dots + a_m = 10m$. Prove that
$$
(a_1 a_2 a_3 \cdots a_m)^{1/m} \le 3\sqrt{11}.
$$
$$
(a_1 a_2 a_3 \cdots a_m)^{1/m} \le 3\sqrt{11}.
$$