Question

Which of the following equations has only one solution? please show work

Answer 1

In x^2=9, you have to square root it, but there's a catch - it's a plus or minus with the square root because it can either be 3 or -3 in this scenario, so
x= +-3=+- sqrt(9)

In x(x-1)=9, we have x^2-x=9 when expanding, which turns into x^2-x-9=0. Using the quadratic formula, we have x=(1+-sqrt(1+36))/2, which is (1+-sqrt(37)/2) for x, and that has 2 solutions given the plus and minus. 

For the third one, we have x^2-6x-9=0. Factoring it, we get (x-3)^2=0, and that clearly has only one answer - x=3