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प्रश्न
Write two Pythagorean triplets each having one of the numbers as 5.
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उत्तर
Given: We know that for any natural number greater than 1, (2m, m2 – 1, m2 + 1) is a the Pythagorean triplet.
So if one number is m2 + 1 then other two number are m2 – 1 and 2m.
i.e. m2 + 1 = 5 ...(Given)
⇒ m2 = 4
⇒ m = 2
Then m2 – 1
= 22 – 1
= 4 – 1
= 3
And 2m = 2(2) = 4
Hence, Pythagorean triplet is 3, 4 and 5
Similarly another triplet is:
- We need a2 + b2 = c2
- Let's try b = 12 and solve for c:
- 52 + 122 = 25 + 144 = 169
- c2 = 169
- c = `sqrt(169)` = 13
Thus, the triplet is (5, 12, 13).
Hence, 3, 4, 5 and 5, 12, 13 are two Pythagorean triplet.
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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.
Which of the following triplets are pythagorean?
(8, 15, 17)
Which of the following triplet is pythagorean?
(18, 80, 82)
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:
1 + 2 + 3 + 4 + 5 + ... + 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 :
12 + 22 + 32 + 42 + ... + 102
Which of the following number square of even number?
5476
Find the square of the following number:
127
Find the square of the following number:
425
The sum of two perfect squares is a perfect square.
