SOLUTION: how many ordered pairs (x,y) of positive integers satisfy the equation x^4y^4-10x^2y^2+9=0 Please help. Thank You :>

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Question 827184: how many ordered pairs (x,y) of positive integers satisfy the equation x^4y^4-10x^2y^2+9=0
Please help. Thank You :>
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
           x4y4-10x²y²+9 = 0

        (x²y²-9)(x²y²-1) = 0

(xy-3)(xy+3)(xy-1)(xy+1) = 0

xy-3 = 0
  xy = 3

Integer solutions
(3,1), (-3,-1), (1,3), (-1,-3)

xy+3 = 0
  xy = -3

Integer solutions
(3,-1), (-3,1), (1,-3), (-1,3)

xy-1 = 0
  xy = 1

Integer solutions
(1,1), (-1,-1)

xy+1 = 0
  xy = -1

Integer solutions
(1,-1), (-1,1)

Total:

(3,1), (-3,-1), (1,3), (-1,-3), 
(3,-1), (-3,1), (1,-3), (-1,3), 
(1,1), (-1,-1), (1,-1), (-1,1)

I count 12.

Edwin
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