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.

Question 1051119: 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 Edwin McCravy(20066) (Show Source): You can put this solution on YOUR website!




Add the two equations:



Factor both sides:



x and y do not have the same absolute values,
therefore (x+y) does not equal 0 and we may divide
both sides by it.



------------------------------------------



Subtract the two equations:



Factor both sides:



x and y do not have the same absolute values,
therefore (x-y) does not equal 0 and we may divide
both sides by it.



--------------------------

Now we have the two equations:




Subtract them and get

      

      

Answer: -7

Edwin

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