Question 9
Given an integer number $n \ge 3$, determine the maximum value the product of $n$ non-negative real numbers $x_1, x_2, \dots, x_n$ may achieve, subject to
$$
\frac{x_1}{1+x_1} + \frac{x_2}{1+x_2} + \dots + \frac{x_n}{1+x_n} = 1.
$$
$$
\frac{x_1}{1+x_1} + \frac{x_2}{1+x_2} + \dots + \frac{x_n}{1+x_n} = 1.
$$