Question 88
Let $a$, $b$, $c$ be positive real numbers. Prove that
$$
\frac{1}{abc} + 1 \geq 3 \left( \frac{1}{a^2 + b^2 + c^2} + \frac{1}{a + b + c} \right).
$$
$$
\frac{1}{abc} + 1 \geq 3 \left( \frac{1}{a^2 + b^2 + c^2} + \frac{1}{a + b + c} \right).
$$