DANUBE 2010 Problem 5

Let $n\ge3$ be a positive integer. Find the real numbers $x_1\ge0,\ldots,x_n\ge 0$ , with $x_1+x_2+\ldots +x_n=n$ , for which the expression $$(n-1)(x_1^2+x_2^2+\ldots+x_n^2)+nx_1x_2\ldots x_n$$ takes a minimal value.