Question 45
Let $a$, $b$, and $c$ be positive real numbers such that $ab + bc + ca = 3$. Show that
$$
\frac{bc}{1 + a^{4}} + \frac{ca}{1 + b^{4}} + \frac{ab}{1 + c^{4}} \geq \frac{3}{2}
$$
$$
\frac{bc}{1 + a^{4}} + \frac{ca}{1 + b^{4}} + \frac{ab}{1 + c^{4}} \geq \frac{3}{2}
$$