algebra

The following identity can be used to find Pythagorean triples, where the expressions x2−y2, 2xy, and x2+y2 represent the lengths of three sides of a right triangle; x and y are positive integers; and x>y.
(x2−y2)2+(2xy)2=(x2+y2)2
If the sides of a right triangle are 57, 176, and 185, what are the values of x and y?
Select two answers: one for x and one for y.

15
10
16
9
8
11

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  1. so, you have
    (x^2-y^2)^2 = 57^2
    (2xy)^2 = 176^2
    so,
    x^4 - 2x^2y^2 + y^4 + 4x^2y^2 = 185^2
    But that is
    (x^2+y^2)^2 = 185^2
    Now you have
    x^2-y^2 = 57
    x^2+y^2 = 185
    adding, 2x^2 = 242
    x^2 = 121
    x = 11
    now you can find y.

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    oobleck
  2. kids

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  3. this website lol

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