Question

Consider any natural number m > 1.We find that (2m, m² – 1, m² + 1) will form a Pythagorean triplet. (A little algebra can help you to verify this!). With this formula, generate a few Pythagorean triplets.

Answer 1

For any natural number m, we have 2m, m² – 1, m² + 1 is a Pythagorean triplet.

(i) Consider 2m = 16 ⇒ m = 8

m² – 1 = 64 – 1 = 63
m² + 1 = 64 + 1 = 65

So Pythagorean triplet is 16, 63, 65.

(ii) Consider 2m = 18 ⇒ m = 9

m² – 1 = 81 – 1 = 80
m² + 1 = 81 + 1 = 82

So Pythagorean triplet is 18, 80, 82.