Single correct option
For x > −2, the minimum value of (x² + 4x + 13)/(x + 2) is
- A. 4
- B. 6
- C. 8
- D. 9
Show answer and solution
Answer: (B) 6
Put t = x + 2 > 0. Then x² + 4x + 13 = (x + 2)² + 9 = t² + 9.
Expression = (t² + 9)/t = t + 9/t.
By AM ≥ GM, t + 9/t ≥ 2√9 = 6, with equality at t = 3 (x = 1).
Minimum value = 6.
Tip: Complete the square around the denominator, then apply AM–GM to t + k/t (minimum 2√k).
Expression = (t² + 9)/t = t + 9/t.
By AM ≥ GM, t + 9/t ≥ 2√9 = 6, with equality at t = 3 (x = 1).
Minimum value = 6.
Tip: Complete the square around the denominator, then apply AM–GM to t + k/t (minimum 2√k).
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