Question 73
Prove that for positive real numbers $a, b, c$ the following inequality holds:
$$
(16a^2 + 8b + 17)(16b^2 + 8c + 17)(16c^2 + 8a + 17) \geq 2^{12}(a+1)(b+1)(c+1).
$$
When does equality hold?
$$
(16a^2 + 8b + 17)(16b^2 + 8c + 17)(16c^2 + 8a + 17) \geq 2^{12}(a+1)(b+1)(c+1).
$$
When does equality hold?