what is pythagoean triplets?

 

 Three numbers are said to be Pythagorean triplet, if they satisfy the Pythagoras theorem.

 

We may get Pythagorean triplets by using general formula 2m, m ² – 1, m ² + 1, where m is a natural number.

(1)

Let m ² – 1 = 3

⇒ m ² = 4

⇒ m = 2

∴ 2m = 2 × 2 = 4 and m ² + 1 = 2² + 1 = 4 + 1 = 5

Thus, the triplet is 3, 4, and 5.

 

(2)

Let m ² – 1 = 16

⇒ m ² = 16 + 1 = 17

We will not get an integer value of m.

We try to take m ² + 1 = 16

⇒ m ² = 16 – 1 = 15

Again, we will not get an integer value of m.

Now, we take 2m = 16

⇒ m = 8

When m = 8,

m ² – 1 = 8² – 1 = 64 – 1 = 63 and m ² + 1 = 8² + 1 = 64 + 1 = 65

Thus, the triplet is 16, 63, and 65.