Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises - Page 148: 101

$\{-\frac{1}{27}, \frac{1}{8}\}$

Step 1. Let $u=(x)^{-1/3}$, we have $u^2+u-6=0$ Step 2. Factor and solve: $(u-2)(u+3)=0$ thus $u=-3, 2$ Step 3. For $u=-3$, we have $(x)^{-1/3}=-3$ thus $x=-\frac{1}{27}$ Step 4. For $u=2$, we have $(x)^{-1/3}=2$ thus $x=\frac{1}{8}$ Step 5. Solution set $\{-\frac{1}{27}, \frac{1}{8}\}$