求证二重不等式

lihpb04

\(x_i\)和\(y_{ij}\)为任意正实数，i、j∈{0,1,2,...,n}且i≠j,\(y_{ij}\)=\(y_{ji}\)。求证


\(\sum_{0\le i<j\le n}^{ }x_ix_j\sum_{k=0;k\ne i{,}j}^ny_{ik}y_{jk}\le\frac{1}{2}\sum_{0\le i<j\le n}^{ }\left( nx_i^2+nx_j^2-2x_ix_j\right)y_{ij}^2\)