Question 57
If $a$, $b$, $c$ are positive real numbers such that $a^2 + b^2 + c^2 = 1$, show that
$$
\frac{bc}{2 - a^2} + \frac{ca}{2 - b^2} + \frac{ab}{2 - c^2} \le \frac{3}{5}.
$$
$$
\frac{bc}{2 - a^2} + \frac{ca}{2 - b^2} + \frac{ab}{2 - c^2} \le \frac{3}{5}.
$$