Question 84
Let $a$, $b$, $c$ be positive real numbers such that $a + b + c = 1$. Prove that
$$
\frac{7 + 2b}{1 + a} + \frac{7 + 2c}{1 + b} + \frac{7 + 2a}{1 + c} \geq \frac{69}{4}.
$$
When does equality hold?
$$
\frac{7 + 2b}{1 + a} + \frac{7 + 2c}{1 + b} + \frac{7 + 2a}{1 + c} \geq \frac{69}{4}.
$$
When does equality hold?