Question

write a pythogorean triplet whose one of the member is 32​

Answer 1

Answer:

32, 24, 40

Step-by-step explanation:

You can make a pythagorean triplet of any even number, x, by squaring x to get x², then dividing x² by four, to get x²/4 then adding 1 to the result x²/4 +1, and then subtracting one from the result x²/4 - 1.

32² => 1024 => 1024/4 => 256 => 256 + 1 = 257, 256 - 1 = 255: 32, 255, 257

But 32/2 = 16 which is even so:

16² => 256 => 256/4 => 64 => 64 + 1 = 65, 64 - 1 = 63: 2 x ( 16, 63, 65) = 32, 126, 130

But 32/4 = 8 which is even so:

8² => 64 => 64/4 => 16 => 16 + 1 = 17, 16 - 1 = 15: 4 x ( 8, 15, 17) = 32, 60, 68

But 32/8 = 4 which is even so:

4² => 16 => 16/4 => 4 => 4 + 1 = 5, 4 - 1 = 3: 8 x ( 4, 3, 5) = 32, 24, 40

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Answer 2

Pythagorean triplets:

For any natural number m > 1, we have (2m) ² + (m2 – 1)²= (m2 + 1)² . So, 2m, m² – 1 and m² + 1 forms a Pythagorean triplet.

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Solution:

i)

Let  2m = 6

 m = 3

m²+ 1 = 3² + 1= 9 + 1 = 10

m²- 1 = 3 2 - 1 = 9 - 1 = 8

check:

6 ² + 8² = 36 + 64 = 100 = 10²

Hence, the triplet is 6, 8 & 10 

ii)

Let  2 m = 14

 m = 7

 m² + 1 = 7²+ 1 = 49 + 1 = 50

m²- 1 = 7² - 1 = 49 - 1 = 48

check:

14² + 48² = 196 + 1304 = 2500 = 50²

Hence, the triplet is 14, 48, and 50 

iii)

Let 2 m = 16,

 m = 8

 m² + 1 = 8² + 1 = 64 + 1 = 65

m²- 1 = 8 2 - 1 = 64 - 1 = 63

check:

16² + 63² = 256 + 3969 = 4225 = 65²

Hence, the triplet is 16, 63 & 65 

 

iv)

Let  2 m = 18

 

m = 9

m² + 1 = 9² + 1 = 81 + 1 = 82

 m² - 1 = 9² - 1 = 81 - 1 = 80

check:

18²+ 80² = 324 + 6400 = 6724 = 82²

Hence, the triplet is 18, 80 & 82 

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