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Question 210020
JEE Mathematics · Hard

Sequences and Series: AM-GM application MCQ

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AM-GM applicationHardQuestion 210020

Question

For positive reals x and y with x + y = 10, the maximum value of xy is:
  1. A
    20
  2. B
    25
    Correct
  3. C
    30
  4. D
    50

Correct answer

25

Explanation

By AM-GM: (x+y)/2 ≥ √(xy) → 5 ≥ √(xy) → xy ≤ 25. Maximum is 25 when x = y = 5.

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