Question 24
Given an integer $n \ge 3$, determine the least value the sum $\sum_{i=1}^{n} (1/x_i - x_i)$ may achieve, as the $x_i$ run through the positive real numbers subject to $\sum_{i=1}^{n} \frac{1}{x_i + n - 1} = 1$. Also, determine the $x_i$ at which this minimum is achieved.