Question 61
Let $a$, $b$, $c$ be positive real numbers such that $a b c = 1$. Prove the following inequality
$$
\left(\frac{a}{1+a b}\right)^{2}+\left(\frac{b}{1+b c}\right)^{2}+\left(\frac{c}{1+c a}\right)^{2} \geq \frac{3}{4}
$$
$$
\left(\frac{a}{1+a b}\right)^{2}+\left(\frac{b}{1+b c}\right)^{2}+\left(\frac{c}{1+c a}\right)^{2} \geq \frac{3}{4}
$$