Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Practice - Page 783: 5

$x=8, 125$

$x^{2/3}-7x^{1/3}+10=0$ $(x^{1/3})^2-7x^{1/3}+10=0$ $x^{1/3}=y$ $(x^{1/3})^2-7x^{1/3}+10=0$ $y^2-7y+10=0$ $(y-2)(y-5)=0$ $y-2=0$ $y=2$ $y-5=0$ $y=5$ $x^{1/3}=y$ $x^{1/3}=2$ $(x^{1/3})^3=2^3$ $x=2^3$ $x=8$ $x^{1/3}=y$ $x^{1/3}=5$ $(x^{1/3})^3=5^3$ $x=5^3$ $x=125$