Nemotron-IMO-Bench 2026 A28

Let $n$ be a positive integer and let $a\in (0,1)$. What is the minimal value of $x_0^2+...+x_n^2$ among all tuples $(x_0,...,x_n)$ of positive real numbers with sum $n+a$ and such that $\sum_{i=0}^n \frac{1}{x_i}=n+\frac{1}{a}$?