College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.6 - Other Types of Equations and Applications - Summary Exercises on Solving Equations - Page 136: 20

Answer

$x=1$

Work Step by Step

We are given: $-x^{-2}+2x^{-1}=1$ $-x^{-2}+2x^{-1}-1=0$ We multiply through by -1: $-1(-x^{-2}+2x^{-1}-1)=-1(0)$ $x^{-2}-2x^{-1}+1=0$ We multiply through again by $x^2$: $x^2(x^{-2}-2x^{-1}+1)=x^2(0)$ $1-2x+x^2=0$ $x^2-2x+1=0$ And factor: $(x-1)(x-1)=0$ $(x-1)^2=0$ Equate each factor to zero, tehn solve each equation for $x$: $x-1=0$ $x=1$
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