$\displaystyle y = x^{1/3} - x^2 $
How do I solve this equation to find the roots. It's not a quadratic equation because it involves cubic root of x.
Hi there!
I would try:
$\displaystyle 0 = x^{1/3} - x^2$
$\displaystyle x^2 = x^{1/3}$
next step: (both sides)^3
$\displaystyle (x^2)^3 = x^1$
$\displaystyle x^6 = x^1$
$\displaystyle 0 = x^6 - x^1$
$\displaystyle 0 = x (x^5 - 1)$
=> x = 0 or x=1 (solving $\displaystyle x^5 = 1$ leads to x = 1)