Question 65
Let $a$, $b$, $c$ and $d$ be positive real numbers. Prove the inequality
$$
\left(\frac{a}{a+b}\right)^{5} + \left(\frac{b}{b+c}\right)^{5} + \left(\frac{c}{c+d}\right)^{5} + \left(\frac{d}{d+a}\right)^{5} \ge \frac{1}{8}
$$
$$
\left(\frac{a}{a+b}\right)^{5} + \left(\frac{b}{b+c}\right)^{5} + \left(\frac{c}{c+d}\right)^{5} + \left(\frac{d}{d+a}\right)^{5} \ge \frac{1}{8}
$$