Factor Fourth Degree Equation

The number of distinct ordered pairs (x, y), where x and y have positive integral values satisfying the equation x4y4 – 10x2y2 + 9 = 0, is:

  1. 0
  2. 3
  3. 4
  4. 12
  5. infinite


Show/Hide Solution

x4y4 – 10x2y2 + 9 = 0 = (x2y2 – 9) · (x2y2 – 1)

→  (xy + 3)    · (xy – 3)    · (xy + 1)    · (xy – 1)  = 0
  xy = -3
no good
xy = 3
(1, 3)
(3, 1)
(-1, -3)
(-3, -1)
xy = -1
no good
xy = 1
(-1, -1)
(1, 1)
 

So there are 3 solutions. The answer is (b).

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