Question

The identity (x2 + y2) = (x2 -y2) + (2xy)? can be used to generate Pythagorean triples. What

Answer 1

Answer:

48, 55, 73

Step-by-step explanation:

A Pythagorean triple are integers that can be entered in the Pythagorean theorem and be true

A common example is 3, 4, 5 because

$3^{2} +4^{2} =5^{2}$

So here, you want to plug in the 8 for the x in the equation and 3 for the y

Then, what you are looking for is when the equation looks like

$a^{2} + b^{2} = c^{2}$

So:

$(8^{2}+3^{2})^{2} = (8^{2} - 3^{2})^{2} + (2(8)(3))^{2}$

Simplify:

$73^{2} = 55^{2} + 48^{2}$

We can see that the numbers in here follow the pythagorean theorem, where c = 73, b = 55, and a = 48

So the triple is 48, 55, and 73