Question
Question
Use the polynomial identity (x^2+y^2)^2=(x^2−y^2)^2+(2xy)^2
to generate a Pythagorean triple when x equals 7 and y equals 4. Write the Pythagorean triple in ascending order.
Use the polynomial identity (x^2+y^2)^2=(x^2−y^2)^2+(2xy)^2
to generate a Pythagorean triple when x equals 7 and y equals 4. Write the Pythagorean triple in ascending order.
Answers
Answer
Question
Use the polynomial identity (x2+y2)2=(x2−y2)2+(2xy)2
to generate a Pythagorean triple when x equals 7 and y equals 4. Write the Pythagorean triple in ascending order.
Use the polynomial identity (x2+y2)2=(x2−y2)2+(2xy)2
to generate a Pythagorean triple when x equals 7 and y equals 4. Write the Pythagorean triple in ascending order.
Answered by
GPT 3.5
To generate a Pythagorean triple using the given polynomial identity, we can substitute x = 7 and y = 4.
Substituting x = 7 and y = 4 into the polynomial identity, we get:
(7^2 + 4^2)^2 = (7^2 - 4^2)^2 + (2 * 7 * 4)^2
(49 + 16)^2 = (49 - 16)^2 + (56)^2
(65)^2 = (33)^2 + (56)^2
4225 = 1089 + 3136
The equation 4225 = 4225 is true.
Therefore, by substituting x = 7 and y = 4 into the polynomial identity, we have generated the Pythagorean triple (33, 56, 65) in ascending order.
Substituting x = 7 and y = 4 into the polynomial identity, we get:
(7^2 + 4^2)^2 = (7^2 - 4^2)^2 + (2 * 7 * 4)^2
(49 + 16)^2 = (49 - 16)^2 + (56)^2
(65)^2 = (33)^2 + (56)^2
4225 = 1089 + 3136
The equation 4225 = 4225 is true.
Therefore, by substituting x = 7 and y = 4 into the polynomial identity, we have generated the Pythagorean triple (33, 56, 65) in ascending order.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.