Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 787: 24

$x= -64, 1/27$

$3x^{2/3}+11x^{1/3}=4$ $3x^{2/3}+11x^{1/3}-4=4-4$ $3x^{2/3}+11x^{1/3}-4=0$ $y=x^{1/3}$ $3x^{2/3}+11x^{1/3}-4=0$ $3(x^{1/3})^2+11x^{1/3}-4=0$ $3y^2+11y-4=0$ $(3y-1)(y+4)=0$ $3y-1=0$ $3y=1$ $3y/3=1/3$ $y=1/3$ $y+4=0$ $y=-4$ $y=x^{1/3}$ $1/3=x^{1/3}$ $(1/3)^3=(x^{1/3})^3$ $1/27=x$ $y=x^{1/3}$ $-4=x^{1/3}$ $(-4)^3=(x^{1/3})^3$ $-64=x$