SOLUTION: The cube root of x-1 = the cube root of x^2+ 2x -21

Question 27424: The cube root of x-1 = the cube root of x^2+ 2x -21
Answer by mbarugel(146) (Show Source): You can put this solution on YOUR website!
We have that the cube root of x-1 = the cube root of x^2+ 2x -21
But since the sube root of a number is unique (as opposed to the square root, which has two possible solutions) this implies that:
x-1 = x^2+ 2x -21
Writing it as a standard quadratic equation, we get:

And now we solve it using the standard procedure:

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=81 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4, -5. Here's your graph:

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