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प्रश्न
Write the Pythagorean triplet whose one of the numbers is 4.
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उत्तर
For any natural number greater than 1, (2m, m2 – 1, m2 + 1) is Pythagorean triplets.
So, if one number is 2m, then another two numbers will be m2 – 1 and m2 + 1.
Given, one number = 4
Then Pythagorean triplets:
2m = 4 or m = 2
So, m2 – 1 = (2)2 – 1 = 4 – 1 = 3
m2 + 1 = (2)2 + 1 = 4 + 1 = 5
Now, (3)2 + (4)2 = (5)2
⇒ 9 + 16 = 25
⇒ 25 = 25
Therefore, Pythagorean triplets are 3, 4 and 5.
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\[ 1^2 + 2^2 + 3^2 = \frac{1}{6}\left[ 3 \times \left( 3 + 1 \right) \times \left( 2 \times 3 + 1 \right) \right]\]
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