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Qhere are three consecutive odd numbers whose squares have a sum of 2531. Determine the values of these numbers.

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#4479Q ID
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  • A 27, 29, 31 ✔ ✖
  • B 32, 35, 38 ✔ ✖
  • C 17, 19, 21 ✔ ✖
  • D 21, 24, 26 ✔ ✖
Correct Answer: Option A

Explanation

Given:

The sum of the squares of three consecutive odd numbers is 2531
Find:

The values of these numbers
Let the three consecutive odd numbers be x, x + 2, and x + 4. Then the sum of their squares is given by:

x^2 + (x + 2)^2 + (x + 4)^2 = 2531
Expand and rearrange the terms:

3x^2 + 12x - 2511 = 0
Factor the quadratic equation:

(x - 27)(x + 31) = 0
Solve for x:

x = 27
Therefore, the three numbers are x = 27, x + 2 = 27 + 2 = 29, and x + 4 = 27 + 4 = 31.

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