Write a Pythagorean triplet who senone members is

For any natural number m > 1, 2m, m²-1, m²+1 forms a Pythagorean triplet

(i) If we consider,m² + 1 = 6,then m² = 5

The value of m will not be an integer

Now,

If we consider, m² - 1 = 6,then m² = 7

Again the value of m is not an integer

Let us take 2m = 6

So, m = 3

Hence,the Pythagorean triplets are:

2 x 3, 3² - 1,3² + 1 or 6, 8 ,and 10

(ii) If we consider m² + 1 = 14,then m² = 13

The value of m will not be an integer

If we consider m² - 1 = 14,then m² = 15

Again the value of m is not an integer

Let 2 m = 14

m = 7

Hence, m² - 1 = 49 - 1 = 48 and m² + 1 = 49 + 1 = 50

Hence, the  required Pythagorean triplet is14, 48, and 50

(iii) If we consider m² + 1 = 16 ,then m² = 15

The value of m will not be an integer

If we consider m² - 1 = 16,then m² = 17

Againthevalueofmisnotaninteger

Now ,let 2m = 16

m = 8

Therefore,m²-  1 = 64 -1 = 63 and m² + 1 = 64 + 1 = 65

Therefore,the Pythagorean triplet is 16 , 63, and 65

(iv) If we consider m² + 1 = 18,

m² = 17

Then, the value of m will not be aninteger

If we consider m² - 1 = 18,then m² = 19

Again the value of m is not an integer

So, let2m = 18

m = 9

Thus,m² - 1 = 81 - 1 = 80 and m² + 1 = 81 + 1 = 82

Therefore, the Pythagorean triplet is 18, 80, and 82