# what is pythagoean triplets?

Solution :

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

We may get Pythagorean triplets by using general formula 2

*m*,*m*^{2}– 1,*m*^{2}+ 1, where*m*is a natural number.(1)

Let

*m*^{2}– 1 = 3⇒

*m*^{2}= 4⇒

*m*= 2∴ 2

*m*= 2 × 2 = 4 and*m*^{2}+ 1 = 2^{2}+ 1 = 4 + 1 = 5Thus, the triplet is 3, 4, and 5.

(2)

Let

*m*^{2}– 1 = 16⇒

*m*^{2}= 16 + 1 = 17We will not get an integer value of

*m*.We try to take

*m*^{2}+ 1 = 16⇒

*m*^{2}= 16 – 1 = 15Again, we will not get an integer value of

*m*.Now, we take 2

*m*= 16⇒

*m*= 8When

*m*= 8,*m*

^{2}– 1 = 8

^{2}– 1 = 64 – 1 = 63 and

*m*

^{2}+ 1 = 8

^{2}+ 1 = 64 + 1 = 65

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

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