Question

Which of the following equations has only one solutionx(x-1)=9,x^2-6x+9=0,x^2=9

Answer 1

`x^2-6x+9`

Explanation:

We can check the equations for their answers

`x(x-1)=9\\\\x^2-x=9\\\\x^2-x-9=0\\\\`

The first equation cannot be factored. If you were to apply the quadratic formula, you would get the two solutions,
`x=(1\pm√(37))/(2)`. So this cannot be it

`x^2-6x+9=0\\\\(x-3)^2=0\\\\x-3=0\\\\x=3`

The second equation contains one solution. Let's check the last one.

`x^2=9\\\\√(x^2) =√(9)\\\\x=\pm3`

The third equation contains two solutions. Therefore, the second equation is the correct one.