Home Competitions VN-TST 2011 Problem 3
Let n n n ≥ 3. \geq 3. ≥ 3. n n n x 1 , x 2 , ⋯ x n x_1,x_2,\cdots x_n x 1 , x 2 , ⋯ x n { x 1 ≥ x 2 ≥ ⋯ ≥ x n ; x 1 + x 2 + ⋯ + x n = 0 ; x 1 2 + x 2 2 + ⋯ + x n 2 = n ( n − 1 ) . \left\{\begin{aligned}&\ x_1\ge x_2\ge\cdots \ge x_n;& \ x_1+x_2+\cdots+x_n=0;& \ x_1^2+x_2^2+\cdots+x_n^2=n(n-1).\end{aligned}\right. { x 1 ≥ x 2 ≥ ⋯ ≥ x n ; x 1 + x 2 + ⋯ + x n = 0 ; x 1 2 + x 2 2 + ⋯ + x n 2 = n ( n − 1 ) . S = x 1 + x 2 . S=x_1+x_2. S = x 1 + x 2 .
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