Question 92
Given positive real numbers $a, b, c, d$, with
$$
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} = 1,
$$
prove that
$$
\frac{a+b}{a^2 - ab + b^2} + \frac{b+c}{b^2 - bc + c^2} + \frac{c+d}{c^2 - cd + d^2} + \frac{d+a}{d^2 - da + a^2} \le 2.
$$
$$
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} = 1,
$$
prove that
$$
\frac{a+b}{a^2 - ab + b^2} + \frac{b+c}{b^2 - bc + c^2} + \frac{c+d}{c^2 - cd + d^2} + \frac{d+a}{d^2 - da + a^2} \le 2.
$$