A set of numbers forms a Pythagorean triple if the square of the largest number is equal to the sum of the squares of the other two numbers. In mathematical terms, for a set of numbers \(a\), \(b\), and \(c\) (where \(c\) is the largest), the condition is:
\[ c^2 = a^2 + b^2 \]
Let's check each of the provided sets:
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9, 12, 14
- The largest number is 14.
- \(14^2 = 196\)
- \(9^2 + 12^2 = 81 + 144 = 225\)
- \(196 \neq 225\)
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5, 12, 13
- The largest number is 13.
- \(13^2 = 169\)
- \(5^2 + 12^2 = 25 + 144 = 169\)
- \(169 = 169\) (This is a Pythagorean triple)
-
10, 24, 26
- The largest number is 26.
- \(26^2 = 676\)
- \(10^2 + 24^2 = 100 + 576 = 676\)
- \(676 = 676\) (This is also a Pythagorean triple)
-
6, 8, 11
- The largest number is 11.
- \(11^2 = 121\)
- \(6^2 + 8^2 = 36 + 64 = 100\)
- \(121 \neq 100\)
The sets that form Pythagorean triples are 5, 12, 13 and 10, 24, 26.
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