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.
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.
2 answers
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.
1 answer