The number of distinct ordered pairs (x, y), where x and y have positive integral values satisfying the equation x^{4}y^{4} – 10x^{2}y^{2} + 9 = 0, is:
- 0
- 3
- 4
- 12
- infinite
x^{4}y^{4} – 10x^{2}y^{2} + 9 = 0 = (x^{2}y^{2} – 9) · (x^{2}y^{2} – 1)
→ | (xy + 3) · | (xy – 3) · | (xy + 1) · | (xy – 1) | |
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).