Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 788: 41

$x=-8, 1/8$

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