By letting y = x^1/3, or otherwise, find the values of x for which x^1/3 -2x^-1/3 = 1

In this case, the problem is asking us to solve the equation

by substituting .

First, let's substitute the variable into the original equation:

Now, let's solve:

Now, we aren't done yet. We have to find our answer in terms of the original variable, . To do this, set each value for into the substitution equation we found earlier, :

The solutions for the equation are x = -1, 8.