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Question 210019
JEE Mathematics · Medium

Sequences and Series: AM-GM inequality MCQ

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AM-GM inequalityMediumQuestion 210019

Question

For positive reals a and b, AM ≥ GM means:
  1. A
    (a+b)/2 ≥ √(ab)
    Correct
  2. B
    √(ab) ≥ (a+b)/2
  3. C
    (a+b)/2 = √(ab) always
  4. D
    ab ≥ (a+b)²/4

Correct answer

(a+b)/2 ≥ √(ab)

Explanation

Arithmetic mean is always ≥ geometric mean for positive reals: AM = (a+b)/2 ≥ √(ab) = GM, with equality iff a = b.

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