CN-LEAGUE 2001 Problem 2

If nonnegative reals $x_1, x_2, \ldots, x_n$ satisfy $$\sum_{i=1}^n x_i^2 + 2\sum_{1 \leq k < j \leq n} \sqrt{\frac{k}{j}}x_kx_j = 1$$ what are the minimum and maximum values of $\sum_{i=1}^n x_i$ ?