Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 787: 19

$x=-8, 125$

$x^{2/3}-3x^{1/3}-10=0$ $(x^{1/3})^2-3x^{1/3}-10=0$ $y=x^{1/3}$ $y^2-3y-10=0$ $(y-5)(y+2)=0$ $y-5=0$ $y=5$ $y+2=0$ $y=-2$ $y=x^{1/3}$ $5=x^{1/3}$ $5^3=(x^{1/3})^3$ $125=x$ $-2=x^{1/3}$ $(-2)^3=(x^{1/3})^3$ $-8=x$