Question 61
Let $a$, $b$, $c$, $d$ be positive real numbers satisfying $abcd = 1$. Prove that
$$
(a^2b + b^2c + c^2d + d^2a)(ab^2 + bc^2 + cd^2 + da^2) \geq (a+c)(b+d)(ac+bd+2).
$$
When does equality hold?
$$
(a^2b + b^2c + c^2d + d^2a)(ab^2 + bc^2 + cd^2 + da^2) \geq (a+c)(b+d)(ac+bd+2).
$$
When does equality hold?