Problem: The number of distinct ordered pairs (x,y) where x and y have positive integral values satisfying the equation x4y4−10x2y2+9=0 is:
Answer Choices:
A. 0
B. 3
C. 4
D. 12
E. infinite
Solution:
x4y4−10x2y2+9=(x2y2−1)(x2y2−9)=0∴x2y2=1 or x2y2=9.∴xy=+1 or -1 , xy=+3 or −3 . Ordered pairs of positive integral values satisfying these equations are (1,1),(1,3),(3,1).