Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 787: 23

Answer

$x=-1/8, 27$

Work Step by Step

$2x^{2/3}-5x^{1/3}=3$ $2x^{2/3}-5x^{1/3}-3=3-3$ $2x^{2/3}-5x^{1/3}-3=0$ $x^{1/3}=y$ $2x^{2/3}-5x^{1/3}-3=0$ $2(x^{1/3})^2-5x^{1/3}-3=0$ $2y^2-5y-3=0$ $(2y+1)(y-3)=0$ $2y+1=0$ $2y=-1$ $2y/2=-1/2$ $y=-1/2$ $y-3=0$ $y=3$ $x^{1/3}=y$ $x^{1/3}=-1/2$ $(x^{1/3})^3=(-1/2)^3$ $x=-1/8$ $x^{1/3}=y$ $x^{1/3}=3$ $(x^{1/3})^3=3^3$ $x=27$
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