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प्रश्न
If one member of a pythagorean triplet is 2m, then the other two members are ______.
विकल्प
m, m2 + 1
m2 + 1, m2 – 1
m2, m2 – 1
m2, m + 1
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उत्तर
If one member of a pythagorean triplet is 2m, then the other two members are m2 + 1, m2 – 1.
Explanation:
2m = 4
⇒ m = 2
m2 + 1 = 22 + 1
= 4 + 1
= 5
And m2 – 1 = 22 – 1
= 4 – 1
= 3
Now, 32 + 42 = 52
⇒ 9 + 16 = 25
⇒ 25 = 25
So 3, 4 and 5 are pythagorean triplets.
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संबंधित प्रश्न
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and find the value of
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(10, 24, 26)
Observe the following pattern \[1 = \frac{1}{2}\left\{ 1 \times \left( 1 + 1 \right) \right\}\]
\[ 1 + 2 = \frac{1}{2}\left\{ 2 \times \left( 2 + 1 \right) \right\}\]
\[ 1 + 2 + 3 = \frac{1}{2}\left\{ 3 \times \left( 3 + 1 \right) \right\}\]
\[1 + 2 + 3 + 4 = \frac{1}{2}\left\{ 4 \times \left( 4 + 1 \right) \right\}\]and find the values of following:
31 + 32 + ... + 50
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 :
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348
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