Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 787: 27

$y=-1/5, 1/2$

$20x^{2/3}-6x^{1/3}-2=0$ $20(x^{1/3})^2-6x^{1/3}-2=0$ $x^{1/3}=y$ $20(x^{1/3})^2-6x^{1/3}-2=0$ $20y^2-6y-2=0$ $y=(-b±\sqrt {b^2-4ac})/2a$ $y=(-(-6)±\sqrt {(-6)^2-4*20*-2})/2*20$ $y=(6±\sqrt {36+4*20*2})/40$ $y=(6±\sqrt {36+160})/40$ $y=(6±\sqrt {196})/40$ $y=(6±14)/40$ $y=(6+14)/40$ $y=20/40$ $y=1/2$ $y=(6-14)/40$ $y=-8/40$ $y=-1/5$