Question

How do you solve `x^3-6x^2+6x=0`?

Answer 1

I found:
`x_1=0`
`x_2=3+sqrt(3)`
`x_3=3-sqrt(3)`

Explanation:

We can try collecting `x`:
`x(x^2-6x+6)=0`
you get the first solution from the `x(...)=0` bit which gives you: `x_1=0`
the other two solutions are found solving the `x^2-6x+6=0` bit using the Quadratic Formula:
`x_(2,3)=(6+-sqrt(36-24))/2=(6+-sqrt(12))/2=(6+-2sqrt(3))/2=3+-sqrt(3)`
giving:
`x_2=3+sqrt(3)`
`x_3=3-sqrt(3)`