Question

Which combination of integers can be used to generate the Pythagorean triple (7,24,25)?

Answer 1

it would be b...........

Answer 2

A Pythagorean triple is a set of thre integer numbers, a, b and c that meet the Pythgorean theorem a^2 + b^2 = c^2

Use Euclide's formula for generating Pythagorean triples.

This formula states that given two arbitrary different integers, x and y, both greater than zero, then the following numbers a, b, c form a Pythagorean triple:

a = x^2 - y^2

b = 2xy

c = x^2 + y^2.


From a = x^2 - y^2, you need that x > y, then you can discard options A and D.

Now you have to probe the other options.

Start with option B, x = 4, y = 3

a = x^2 - y^2 = 4^2 - 3^2 = 16 -9 = 7

b = 2xy = 2(4)(3) = 24

c = x^2 9 y^2  = 4^2 + 3^2 = 16 + 9 = 25

Then we could generate the Pythagorean triple (7, 24, 25) with x = 4 and y =3.

If you want, you can check that a^2 + b^2 = c^2; i.e. 7^2 + 24^2 = 25^2

The answer is the option B. x = 4, y = 3