Question 139
Let $x_1, x_2, \dots, x_n$ be positive numbers such that:
$$
x_1^{n-1} + x_2^{n-1} + \dots + x_n^{n-1} = x_1 x_2 \dots x_n
$$
Prove the inequality:
$$
(x_1 - n + 1)(x_2 - n + 1)\dots(x_n - n + 1) \ge 1. \quad (\text{Serdiuk Nazar})
$$
$$
x_1^{n-1} + x_2^{n-1} + \dots + x_n^{n-1} = x_1 x_2 \dots x_n
$$
Prove the inequality:
$$
(x_1 - n + 1)(x_2 - n + 1)\dots(x_n - n + 1) \ge 1. \quad (\text{Serdiuk Nazar})
$$