SOLUTION: Let x and y be real numbers whose absolute values are different and that satisfy x^3 = 20x + 7y y^3 = 7x + 20y Find xy.

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Question 1096469: Let x and y be real numbers whose absolute values are different and that satisfy
x^3 = 20x + 7y
y^3 = 7x + 20y
Find xy.
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!

An unusual problem; I don't recall seeing anything quite like it before....

Add the two equations and do some algebra:
x%5E3%2By%5E3+=+27x+%2B+27y
%28x%2By%29%28x%5E2-xy%2By%5E2%29+=+27%28x%2By%29
x%5E2-xy%2By%5E2+=+27 <-- equation (1)

Then subtract the two equations and do some similar algebra:
x%5E3-y%5E3+=+13x+-+13y
%28x-y%29%28x%5E2%2Bxy%2By%5E2%29+=+13%28x-y%29
x%5E2%2Bxy%2By%5E2+=+13 <-- equation (2)

Now subtract equation (1) from equation (2):
2xy+=+-14
xy+=+-7

Answer: xy = -7