Question

Use the Pythagorean identity. (x2 - y²)2 + (2xy)2 = (x2 + y2)2, to create a Pythagorean triple.

Answer 1

Answer:

Step-by-step explanation:

(x2 - y2)2 + (2xy)2 = (x2 + y2)2

1.   Let x = 2 and y = 1 .

2. x must be greater than y

- as the sides of a triangle must be positive.

 We can enter any positive integer values for x and y as long as x > y because we are dealing with an identity.

3. Then substituting,  we have

(2^2 - 1^2)^2 + (2*2*1)^2 = (2^2 + 1^2)^2

3^2 + 4^2 = 5^2

9 + 16 = 25

25=25

So the triple is 3,4 and 5.

4.  At least one leg must be even because one term (2xy) must be even - multiplying by 2 always gives an even value.