Show that the inequality ∑i=1n∑j=1n∣xi−xj∣⩽∑i=1n∑j=1n∣xi+xj∣\sum_{i=1}^{n} \sum_{j=1}^{n} \sqrt{|x_i - x_j|} \leqslant \sum_{i=1}^{n} \sum_{j=1}^{n} \sqrt{|x_i + x_j|}i=1∑nj=1∑n∣xi−xj∣⩽i=1∑nj=1∑n∣xi+xj∣ holds for all real numbers x1,…,xnx_1, \ldots, x_nx1,…,xn.