To determine which of the provided sets of numbers is not a Pythagorean triple, we need to check which set does not satisfy the equation \( a^2 + b^2 = c^2 \), where \( c \) is the largest number in each set (the hypotenuse of the right triangle).
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Set: 7, 24, 25
- \( 7^2 + 24^2 = 49 + 576 = 625 \)
- \( 25^2 = 625 \)
- This is a Pythagorean triple.
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Set: 6, 9, 12
- \( 6^2 + 9^2 = 36 + 81 = 117 \)
- \( 12^2 = 144 \)
- This is not a Pythagorean triple.
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Set: 9, 40, 41
- \( 9^2 + 40^2 = 81 + 1600 = 1681 \)
- \( 41^2 = 1681 \)
- This is a Pythagorean triple.
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Set: 8, 15, 17
- \( 8^2 + 15^2 = 64 + 225 = 289 \)
- \( 17^2 = 289 \)
- This is a Pythagorean triple.
Based on the calculations above, the set that is not a Pythagorean triple is:
6, 9, 12