Sarkari RiseLogin
CDS 2024 · PYQ · AM-GM Inequality · medium

For a, b > 0, what is the minimum value of ((a² + 3a + 1)/a)((b² + 3b + 1)/b)?

  1. A.1
  2. B.9
  3. C.16
  4. 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.
💡 Practice unlimited CDS PYQs + AI-tracked progress on each topic. Sign up free →

Want more CDS practice?

Free daily 10-Q quiz · adaptive mocks · 4,000+ verified PYQs · AI doubt solver in Hindi + English

Sign up freeMore AM-GM Inequality practice