# Help me solve this equation: $x^\frac23 - 9x^\frac13+8=0$

Not sure what to call this type of equation so please let me know. I'm having trouble solving it though.

Solve the equation: $$x^\frac23 - 9x^\frac13+8=0$$

• You could call it quadratic-like... – DJohnM May 28 '13 at 23:51

Hint: try the substitution $y = x^{\frac{1}{3}}$. This should give you a quadratic.
• Edit: you should get $x^{\frac{1}{3}} = 8$ or $1$ – Alex Wertheim May 28 '13 at 23:16
Hint: put $\,t:=x^{1/3}\,$ and get the easy quadratic
$$0=t^2-9t+8=(t-8)(t-1)\ldots\ldots$$