Question 32
Let $n$ be a positive integer. Prove that for all $x_1, x_2, \dots, x_n \in [0, 1]$ the following holds:
$$
(x_1 + x_2 + \dots + x_n + 1)^2 \ge 4(x_1^2 + x_2^2 + \dots + x_n^2). \quad (\text{ASU 1979})
$$
$$
(x_1 + x_2 + \dots + x_n + 1)^2 \ge 4(x_1^2 + x_2^2 + \dots + x_n^2). \quad (\text{ASU 1979})
$$