Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 788: 38

$x=-8, 64$

$x^{2/3}-2x^{1/3}-8=0$ $(x^{1/3})^2-2x^{1/3}-8=0$ $x^{1/3} =y$ $(x^{1/3})^2-2x^{1/3}-8=0$ $y^2-2y-8=0$ $(y-4)(y+2)=0$ $y-4=0$ $y=4$ $y+2=0$ $y=-2$ $x^{1/3} =y$ $x^{1/3} =4$ $(x^{1/3})^3 =4^3$ $x=64$ $x^{1/3} =y$ $x^{1/3} =-2$ $(x^{1/3})^3 =(-2)^3$ $x=-8$