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Question

Which of the following is/are not Pythagorean triplet (s)?
(a) 3,4,5
(b) 8,15,17
(c) 7,24,25
(d) 13,26,29

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Solution

In (a)
32 + 42 = 52
⇒ 9 + 16 = 25
⇒ 25 = 25
Since, the sum of the square of two smallest number is equal to the square of largest number.
Hence, it is a Pythagorean triplet.
In (b)
82 + 152 = 172
⇒ 64 + 225 = 289
⇒ 289 = 289
Since, the sum of the square of two smallest number is equal to the square of largest number.
Hence, it is a Pythagorean triplet.
In (c)
72 + 242 = 252
⇒ 49 + 576 = 625
⇒ 625 = 625
Since, the sum of the square of two smallest number is equal to the square of largest number.
Hence, it is a Pythagorean triplet.
In (d)
132 + 262 ≠ 292
⇒ 169 + 676≠ 841
⇒ 845 ≠ 841
Since, the sum of the square of two smallest number is not equal to the square of largest number.
Hence, it is not a Pythagorean triplet.
Hence, the correct answer is option (d).

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