Question 56
Let $a$, $b$, $c$ be non-negative real numbers such that $ab + bc + ca = 3$. Suppose that
$$
a^3 b + b^3 c + c^3 a + 2abc(a + b + c) = \frac{9}{2}
$$
What is the minimum possible value of $ab^3 + bc^3 + ca^3$?
$$
a^3 b + b^3 c + c^3 a + 2abc(a + b + c) = \frac{9}{2}
$$
What is the minimum possible value of $ab^3 + bc^3 + ca^3$?