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Question 220024
JEE Mathematics · Medium

Quadratic Equations and Inequalities: Word problem MCQ

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Word problemMediumQuestion 220024

Question

If the sum of the squares of two consecutive natural numbers is 145, the numbers are:
  1. A
    8, 9
    Correct
  2. B
    9, 10
  3. C
    7, 8
  4. D
    10, 11

Correct answer

8, 9

Explanation

Let numbers be n and n+1. n² + (n+1)² = 145 → 2n²+2n+1 = 145 → 2n²+2n−144 = 0 → n²+n−72 = 0 → (n+9)(n−8) = 0 → n = 8. Numbers: 8, 9.

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