write a Pythagorean triple whose one number is
6,14,16 and 18
Answers
Step-by-step explanation:
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.
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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Answer:
General form=
<br> 1)If 2m=6,Then m=3 ,
=8,
=10<br> Triplet=6,8,10<br> 2)If 2m=14,Then m=7,
=48,
=50<br> Triplet=14,48,50<br> 3)If 2m=16, Then m=8,
=63,
=65.