Question 5
Given $x_1,x_2,\ldots,x_n>0$, $n\ge5$, show that
$$\frac{x_1x_2}{x_1^2+x_2^2+2x_3x_4}+\frac{x_2x_3}{x_2^2+x_3^2+2x_4x_5}+\cdots+
\frac{x_nx_1}{x_n^2+x_1^2+2x_2x_3}\le\frac{n-1}{2}.$$
$$\frac{x_1x_2}{x_1^2+x_2^2+2x_3x_4}+\frac{x_2x_3}{x_2^2+x_3^2+2x_4x_5}+\cdots+
\frac{x_nx_1}{x_n^2+x_1^2+2x_2x_3}\le\frac{n-1}{2}.$$