Jamar wants to generate a Pythagorean triple when x equals 12 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 225 225 441 441 3,969 3,969 108
To generate a Pythagorean triple using the given polynomial identity, we can substitute x = 12 and y = 9 into the equation:
(x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2
(12^2 + 9^2)^2 = (12^2 - 9^2)^2 + (2 * 12 * 9)^2
(144 + 81)^2 = (144 - 81)^2 + (216)^2
(225)^2 = (63)^2 + (216)^2
50625 = 3969 + 46656
50625 = 50625
Therefore, the value of the Pythagorean triple is 225.