Q100 of 142 Page 88

Write two Pythagorean triplets each having one of the numbers as 5.

Given:

We know that for any natural number greater than 1, (2m, m²-1, m² + 1) is a the Pythagorean triplet.

So if one number is m² + 1 then other two number are m²-1 and 2m.

i.e. m² + 1 = 5 (given)

⇒ m² = 4

⇒ m = 2

Then m²-1 = 2²-1 = 4-1 = 3

And 2m = 2(2) = 4

Hence, Pythagorean triplet is 3, 4 and 5

Similarly another triplet is:

13² = 12² + 5²

Hence, 3,4,5 and 5,12,13 are two Pythagorean triplet.

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101

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102

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