If x+y=9 and xy=20 find x-y

Question

This is a question from the chapter algebraic expresssions.

Answer 1

xy=20 tells us that y = 20/x.

Substituting, we have x + 20/x = 9

multipllying all terms by x gives x²  +20 = 9x.

This quadratic is x² -9x + 20 = 0 and it can be written (x-4)(x-5) = 0 so there are two values for x: either 4 or 5.

Therefore x-y is either 1 or -1.  Two answers.