2024 · Q60
What is the minimum value of ((a²+3a+1)/(a))((b²+3b+1)/(b)) for a, b > 0?
Elementary MathematicsAlgebra
- A1
- B9
- C16
- D25
Explanation
(a² + 3a + 1)/a = a + 3 + 1/a ≥ 5 by AM–GM, with equality at a = 1; likewise the b-factor is at least 5. Hence the product is at least 25. The value 25 is attained at a = b = 1, option (d).