Question

Pythagorean triplets
Observe the following:
(1) 32 + 4 = 9 + 16 = 25 = 52
: 3² +4² = 52
The collection of numbers (3,4,5) is known as Pythagorean triplet.
(11) 62 +82 = 36 + 64 = 100 = 102
:6² +82 = 10²
(6, 8, 10) is also a Pythagorean triplet.
Thus we can say that
Three natural numbers m, n, p are said to form a Pythagorean triplet (m, n, p) if me+ = p.
For any natural number m > 1, we have
(2m)2 + (m2 - 1)2 = (m? + 1)2
So (2m, m? - 1, m + 1) forms a Pythagorean triplet.








can someone explain this to me? tomorrow is my exam n I'm confused ​

Answer 1

Answer:

from the formula you take any three no. and check them ,when answer is adding two number is equal to third no ,then it is pythagorean triplet

Answer 2

Let us take one set of Pythagorean triplets (8,15,17)

Here,  8^2 +15^2 = 17^2

8^2 +15^2 = 64 +225 = 289 = 17^2

For any positive number denoted as n where n is greater than 1 ,, a set of numbers ( n^2+1 , n^2-1 , 2n ) forms a pythagorean triplet.

Taking n = 4

n^2+1 = 4^2 +1 = 16+1 = 17

n^2-1 = 4^2-1 = 16-1 = 15

2n = 2 ×4 = 8

So the Pythagorean Triplet formed is (8,15,17) which is already prooved before that this set is an pythagorean triplet.

Hope you have understood

Hope it helps