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
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.
To generate a Pythagorean triple using the given polynomial identity (x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2, we can substitute the values of x and y and simplify.
Given: x = 18 and y = 9
Substitute the values into the equation:
(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 + (36)^2
(405 * 405) = (243 * 243) + (36 * 36)
164025 = 59049 + 1296
Now let's check the options to find the value of the Pythagorean triple:
a. 162: This does not match the result we obtained (164025).
b. 324: This does not match the result we obtained (164025).
c. 81: This does not match the result we obtained (164025).
d. 729: This does not match the result we obtained (164025).
None of the given options matches the value of the Pythagorean triple we obtained.
To generate a Pythagorean triple using the given polynomial identity, we need to substitute the values of x and y and simplify the equation.
Given:
x = 18
y = 9
Substituting these values into the polynomial identity, we get:
(18^2 + 9^2)^2 = (18^2 - 9^2)^2 + (2 * 18 * 9)^2
(324 + 81)^2 = (324 - 81)^2 + (2 * 18 * 9)^2
(405)^2 = (243)^2 + (36)^2
164025 = 59049 + 1296
164025 = 60345
Since the equation is not balanced, it means that the given values of x and y do not form a Pythagorean triple.
Therefore, none of the provided answer choices (a, b, c, or d) are correct values of the Pythagorean triple.