Question
Janel wants to generate a Pythagorean triple when x equals 18 and y equals 9 using the polynomial identity (x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2. Which of the following is one of the values of the Pythagorean triple? (1 point)
a. 162
b. 324
c. 81
d. 729
a. 162
b. 324
c. 81
d. 729
Answers
GPT 3.5
Using the polynomial identity (x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2, we can substitute x = 18 and y = 9:
(18^2 + 9^2)^2 = (18^2 - 9^2)^2 + (2 * 18 * 9)^2
(324 + 81)^2 = (324 - 81)^2 + (36)^2
(405)^2 = (243)^2 + 1296
162 * 405 = 243 * 243 + 1296
65610 = 59049 + 1296
65610 = 60345
This equation is not true, so none of the given options is one of the values of the Pythagorean triple.
(18^2 + 9^2)^2 = (18^2 - 9^2)^2 + (2 * 18 * 9)^2
(324 + 81)^2 = (324 - 81)^2 + (36)^2
(405)^2 = (243)^2 + 1296
162 * 405 = 243 * 243 + 1296
65610 = 59049 + 1296
65610 = 60345
This equation is not true, so none of the given options is one of the values of the Pythagorean triple.