write an Pythagorean triplet whose smallest number is 8
Answers
Answer:
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Answer :
We get the Pythagorean triplets by using the General Formula that is [ 2m, m² - 1, n² + 1 ]
First let's take → m² - 1 = 8
→ m² = 8 + 1 = 9
→ m = 3
→ 2m = 6 and m² + 1 = 10
The triplet is therefore 6, 8, 10. hence, 8 is not the smallest method of this.
→ 2m = 8
→ m = 4
→ m² - 1 = 16 - 1 = 15 and
→ m² + 1 = 16 + 1 = 17
The triplet is 8, 18, 17 with 8 as the smallest number.
Similar example for this question:
Question:
Find a Pythagorean triplet in which one member is 12.
Answer :
if we take → m² - 1 = 12
→ m² = 12 + 1 = 13
So, the value of n will not be an integer.
now let's try → m² + 1 = 12
m² = 11 will not give an integer value for m.
→ 2m = 12
→ m = 6
→ m² - 1 = 36 - 1 = 35 and
→ m² + 1 = 36 + 1 = 37
Therefore, the required triplet are 12, 35, 37.
General Note:
All the Pythagorean triplets may not be obtained using this form.