Question

Suppose x, y, and z are different positive integers such that xy, yz, and zx are all perfect

squares. Must x, y, and z be perfect squares? Why or why not?

Answer 1

Answer: Yes, and the numbers are 4, 36, and 9

Explanation:

Yes, because it x=4, y=36, and z=9 then 4 * 36=144, 144=12*12 4*9=36, 36=6*6, and 9*36=324, 324=18*18. As you can see they are all perfect squares and 4, 36, and 9 are all perfect sqaures too.