pythagorean triples are composed of?

Question

a/ integers
b/ natural numbers
c/ rational numbers
d/irrational numbers

Answer 1

The simplest Pythagorean triplets are composed of natural numbers.

But in an isoscles right triangle, Two sides are equal. Let them both be some natural number x. The hypotenuse is [x * sqrt (2)], which is obviously irrational.

One cannot say that these are not triplets. A Pythagorean triplet is a set of 3 numbers a, b and c such that:

a^2 + b^2 = c^2

a, b or c can be rational or irrational. In other words, such triples are composed of real numbers, which is a set of numbers that includes whole numbers, natural numbers, rational numbers and irrational numbers.

Here is a natural number example:

3^2 + 4^2 = 5^2

Here is a triplet composed of one irrational number:

1^2 + 1^2 = (sqrt 2)^2

Here is a completely irrational triplet:

(sqrt 6)^2 + (sqrt 11)^2 = (sqrt 17)^2


The numbers a,b and c that make such triplets are written as (a, b, c) with a < (or equal to) b < c

Answer 2

Well the first one is

3, 4, 5

Answer 3

A Pythagorean triple consists of three positive integers a, b, and c, such that a²+ b² = c². Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5).

Answer 4

Take:

2n+1, and two consecutive numbers m,m+1 such that
(m + 1)^2 - m^2 = (2n + 1)^2

m^2 +2m + 1 - m^2 = (2n + 1)^2

2m + 1 = (2n + 1)^2

2m = (2n + 1)^2 - 1

m = [(2n + 1)^2 - 1]/2
m + 1= [(2n + 1)^2 + 1]/2
For each natural n, take the triplet

2n+1, [(2n + 1)^2 - 1]/2, [(2n + 1)^2 + 1]/2

To get 3,4,5, take n=1
2n+1 = 3
[(2n + 1)^2 - 1]/2 = (3^2 - 1)/2 = 8/2 = 4
[(2n + 1)^2 + 1]/2 = (3^2 + 1)/2 = 10/2 = 5

Another pythagorean triplet is 5,12,13
5=2*2+1

[(2*2 + 1)^2 - 1]/2 = (5^2 - 1)/2 = 24/2 = 12
[(2*2 + 1)^2 + 1]/2 = (5^2 + 1)/2 = 26/2 = 13

And so on...

And choose b - natural numbers as your answer.

Answer 5

A square of "ANY odd whole number" when split as "two values having a-unit difference" ( 'a higher value is a hypotenuse' and 'lower value is a long-side of right angled triangle'), a relation "(any odd number)^2 = (hypotenuse)^2 - (a long-side of right angled triangle)^2 " is maintained!

We know it as Pythagorean triplets!

Answer 6

It consists of three nos like a,b,c such that:a^2+b^2=c^2

here c is the greatest no

this is used in right angled triangles

Answer 7

Three numbers a, b and c such that a^2 + b^2 = c^2.