Question

Write the Pythagorean triplet whose smallest member is 8-

Answer 1

Pythagoras triplet means set of three numbers which follow the Pythagoras theorem.
e.g , Let A = {a, b, c} is a Pythagoras triplet. When a² = b² + c², or b²=c²+a², or c² =b²+a² .
How to find triplet .
step1:- Let 2n= 8 , then,n = 4

step2:- largest number of triplet = 4n+1 . From above n =4 put it here,
Largest number of triplet = 4×4+1 = 17

step3:- middle number of triplet= 4n-1 .now put n = 4 , then,Middle number of triplet= 4×4-1 = 15

Hence, Pythagoras triplet is { 8, 15 , 17} .

You can check it .
8² +15² = 17² , follow Pythagoras theorem.

Answer 2

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.