Dokaži da za sve realne brojeve x1,x2,…,x100x_1, x_2, \ldots, x_{100}x1,x2,…,x100 vrijedi nejednakost
∑1⩽i<j⩽100(xj−xi)2j2−i2⩾1101∑1⩽i⩽50(x101−i−xi)2.\sum_{1 \leqslant i < j \leqslant 100} \frac{(x_j - x_i)^2}{j^2 - i^2} \geqslant \frac{1}{101} \sum_{1 \leqslant i \leqslant 50} (x_{101-i} - x_i)^2.1⩽i<j⩽100∑j2−i2(xj−xi)2⩾10111⩽i⩽50∑(x101−i−xi)2.