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प्रश्न
Write a Pythagorean triplet whose one member is 6.
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उत्तर
The three numbers of the Pythagorean triplet are 2m, m2 - 1 and m2 + 1.
Here, 2m = 6
so, m = 3
Second number (m2 - 1) = (3)2 - 1
= 9 - 1
= 8
Third number (m2 + 1) = (3)2 + 1
= 9 + 1
= 10
Hence the Pythagorean triplet is (6, 8, 10).
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\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :
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