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प्रश्न
Write a Pythagorean triplet whose one member is 14.
उत्तर
The three numbers of the Pythagorean triplet are 2m, m2 - 1, and m2 + 1.
Here, 2m = 14
so, m = 7
Second number (m2 - 1) = (7)2 - 1
= 49 - 1
= 48
Third number (m2 + 1) = (7)2 + 1
= 49 + 1
= 50
Hence the Pythagorean triplet is (14, 48, 50).
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संबंधित प्रश्न
Write a Pythagorean triplet whose one member is 18.
From the pattern, we can say that the sum of the first n positive odd numbers is equal to the square of the n-th positive number. Putting that into formula:
1 + 3 + 5 + 7 + ... n = n2, where the left hand side consists of n terms.
Observe the following pattern \[1^2 = \frac{1}{6}\left[ 1 \times \left( 1 + 1 \right) \times \left( 2 \times 1 + 1 \right) \right]\]
\[ 1^2 + 2^2 = \frac{1}{6}\left[ 2 \times \left( 2 + 1 \right) \times \left( 2 \times 2 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 = \frac{1}{6}\left[ 3 \times \left( 3 + 1 \right) \times \left( 2 \times 3 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :
52 + 62 + 72 + 82 + 92 + 102 + 112 + 122
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Find the square of the following number:
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The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is ______.
