Question

Janel wants to generate a Pythagorean triple when x equals 18 and y equals 9 using the polynomial identity (x2+y2)2=(x2−y2)2+(2xy)2
. Which of the following is one of the values of the Pythagorean triple?(1 point)
Responses

162
162

324
324

81
81

729

Answer 1

Using the polynomial identity, we have:

(x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2
(18^2 + 9^2)^2 = (18^2 - 9^2)^2 + (2*18*9)^2
(405)^2 = (243)^2 + (324)^2
165025 = 59049 + 104976
165025 = 163025

So, the correct answer is 324.