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प्रश्न
For every natural number m, (2m – 1, 2m2 – 2m, 2m2 – 2m + 1) is a pythagorean triplet.
विकल्प
True
False
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उत्तर
This statement is False.
Explanation:
∵ (2m – 1)2 ≠ (2m2 – 2m)2 + (2m2 – 2m + 1)2
(2m2 – 2m)2 ≠ (2m – 1)2 + (2m2 – 2m + 1)2
And (2m2 – 2m + 1)2 ≠ (2m – 1)2 + (2m2 – 2m)2
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संबंधित प्रश्न
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\[ 1^2 + 2^2 = \frac{1}{6}\left[ 2 \times \left( 2 + 1 \right) \times \left( 2 \times 2 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 = \frac{1}{6}\left[ 3 \times \left( 3 + 1 \right) \times \left( 2 \times 3 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :
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