Question

What are pythagoras triplets?

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Answer 1

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c².

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Answer 2

HEYA, BUDDY !!

→ The 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.

Cheers !