Question 83
Show that, for all positive real numbers $a$, $b$, $c$, and $d$ the following inequality holds:
$$
\sum_{cyc} \frac{a^4}{a^3 + a^2 b + ab^2 + b^3} \ge \frac{a+b+c+d}{4}.
$$
$$
\sum_{cyc} \frac{a^4}{a^3 + a^2 b + ab^2 + b^3} \ge \frac{a+b+c+d}{4}.
$$