RO-NMO 2000 Problem 93

Let be a natural number $n\ge 2$ and an expression of $n$ variables $$E\left( x_1,x_2,...,x_n\right) =x_1^2+x_2^2+\cdots +x_n^2-x_1x_2-x_2x_3-\cdots -x_{n-1}x_n -x_nx_1.$$ Determine $\sup_{x_1,...,x_n\in [0,1]} E\left( x_1,x_2,...,x_n\right)$ and the specific values at which this supremum is attained.