CMO 1998 Problem 6

Let $x_1,x_2,\ldots ,x_n$ be real numbers, where $n\ge 2$ , satisfying $\sum_{i=1}^{n}x^2_i+ \sum_{i=1}^{n-1}x_ix_{i+1}=1$ . For each $k$ , find the maximal value of $|x_k|$ .