Question 133
Real numbers $a_1, a_2, \dots, a_n$ satisfy the following conditions $a_1 + a_2 + \dots + a_n = n$ and $a_1 \ge a_2 \ge \dots \ge a_n \ge 0$. Prove the inequality:
$$
na_1 \ge a_1^2 + a_2^2 + \dots + a_n^2.
$$
$$
na_1 \ge a_1^2 + a_2^2 + \dots + a_n^2.
$$