Question 55
Let $a, b, c \ge 2$ be real numbers, satisfying the condition $a + b + c = \frac{1}{a} + \frac{1}{b} + \frac{1}{c} + 8$. Prove that we have the inequality
$$
3(ab + bc + ca) \le 81 \le (a + b + c)^2.
$$
$$
3(ab + bc + ca) \le 81 \le (a + b + c)^2.
$$