Question 31
Let $a, b, c \gt 0$. Prove that
$$
\frac{2}{(1+a)^2} + \frac{2}{(1+b)^2} + \frac{2}{(1+c)^2} \ge \frac{1}{1+ab} + \frac{1}{1+bc} + \frac{1}{1+ca}
$$
with equality if and only if $a = b = c = 1$.
$$
\frac{2}{(1+a)^2} + \frac{2}{(1+b)^2} + \frac{2}{(1+c)^2} \ge \frac{1}{1+ab} + \frac{1}{1+bc} + \frac{1}{1+ca}
$$
with equality if and only if $a = b = c = 1$.