For a, b > 0, what is the minimum value of ((a² + 3a + 1)/a)((b² + 3b + 1)/b)?
A.1
B.9
C.16
D.25✓ Correct
Explanation
(a² + 3a + 1)/a = a + 3 + 1/a. By AM-GM, a + 1/a ≥ 2, so a + 3 + 1/a ≥ 5, minimum at a = 1. Similarly for b: minimum is 5. Product minimum = 5 × 5 = 25.
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