I'm working through an exercise with the question:
Use substitution to solve for $x$ in the following equation
$x^6 – 4x^3 + 4 = 0$
The solution given is $\sqrt[3]2$ however there is no working in between shown and I'm at a loss for how to arrive at this.
I started trying to factor our the polynomials $x^6$ and $4x^3$ but that didn't really get me anywhere:
$x^3(x^3 – 4) = -4$ is as far as I got.
How can I arrive at $\sqrt[3]2$ with each step shown in between?
Best Answer
Hint: put $y = x^3$, and you get a quadratic equation.