Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - Chapter 1 Test Prep - Review Exercises - Page 179: 69

Answer

$ 1$ and $ 4$.

Work Step by Step

Given $(x-2)^{2/3}=x^{1/3}$, raise both sides to the $3rd$ power to get $((x-2)^{2/3})^3=(x^{1/3})^3$ or $(x-2)^2=x$, thus $x^2-4x+4=x$, $x^2-5x+4=0$ which gives $x=1$ and $x=4$.
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