FIND THE PGT TRIPLET-

WHOSE GREATEST MEMBER IS 101.(METHOD)

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

If we take m² + 1 = 101

then

m² = 101-1

m² =100

m=10

The value of m is an integer.

Now, 

m² − 1 = 101

⇒ m² = 101+1

⇒ m² =102

The value of m is not an integer.

Let 2m = 101

m = 101/2

The value of m is not an integer.

Therefore, the Pythagorean triplets are 2 × 10, 10² − 1, 10² + 1 or 20,99 and 101.