Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises - Page 148: 91

$\{-63,28\}$

Step 1. Let $u=(x-1)^{1/3}$, we have $u^2+u-12=0$ Step 2. Factor and solve: $(u+4)(u-3)=0$ thus $u=-4, 3$ Step 3. For $u=-4$, we have $(x-1)^{1/3}=-4$ or $x-1=-64$ and $x=-63$ Step 4. For $u=3$, we have $(x-1)^{1/3}=3$ or $x-1=27$ and $x=28$ Step 5. Solution set $\{-63,28\}$