My sister asked me for some help on her algebra homework the other day, and I was stumped by her question. The problem is to find the root of $\sqrt[3]{x^2} + \sqrt[3]{x} = 2$.
The internet tells me that x is 1, but I can't seem to figure out why.
I've tried to manipulate it a couple of ways and I always end up with something more complex than when I started like $8 - 12x^{1/3} + 6x^{2/3} - x - x^2 = 0$.
The simplest form I've found is $x^{2/3} + x^{1/3} - 2 = 0$ which reminds me of the quadratic formula a little, but the exponents are rational, not quite what I need.
Any advice on how to proceed?