Question

The identity (x2−y2)2+(2xy)2=(x2+y2)2 is used to create Pythagorean triples, where the expressions x2−y2, 2xy, and x2+y2 represent the lengths of three sides of a right triangle; x and y are positive integers; and x>y.

(x2−y2)2+(2xy)2=(x2+y2)2
What is the Pythagorean triple if x=8 and y=3?

Answer 1

The Pythagorean triple when x=8 and y=3 is (55, 48, 73).

Step-by-step explanation:

The Pythagorean triple can be found by substituting the values of x and y into the equation (x^2 - y^2)^2 + (2xy)^2 = (x^2 + y^2)^2:

(8^2 - 3^2)^2 + (2(8)(3))^2 = (8^2 + 3^2)^2

(64 - 9)^2 + 48^2 = 64 + 9)^2

(55)^2 + (48)^2 = (73)^2

3025 + 2304 = 5329

5329 = 5329

Therefore, the Pythagorean triple when x = 8 and y = 3 is (55, 48, 73).