Q: here are three consecutive odd numbers whose squares have a sum of 2531. Determine the values of these numbers.
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A
27, 29, 31
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B
32, 35, 38
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C
17, 19, 21
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D
21, 24, 26
A
Answer:
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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