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

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A 27,29,31
B 29,31,33
C 31,35,37
D 31,33,35

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Answer: A. 27,29,31

Let the numbers be x, x + 2, x + 4. x² + (x + 2)² + (x + 4)² = 2531 gives 3x² + 12x + 20 = 2531, so x² + 4x - 837 = 0 and (x - 27)(x + 31) = 0.
x = 27, so the numbers are 27, 29 and 31. (Check: 729 + 841 + 961 = 2531.)

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

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