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Question 210034
JEE Mathematics · Hard

Sequences and Series: Min of sum MCQ

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Min of sumHardQuestion 210034

Question

If a, b are positive with a+b = 1, the minimum of (a + 1/a)² + (b + 1/b)² is:
  1. A
    25/2
    Correct
  2. B
    12.5
  3. C
    50
  4. D
    25

Correct answer

25/2

Explanation

By AM inequality and symmetry: minimum occurs at a = b = 1/2. Each bracket = (1/2 + 2)² = (5/2)² = 25/4. Sum = 25/4 + 25/4 = 25/2.

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