Precalculus (6th Edition)

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

Chapter 1 - Equations and Inequalities - Summary Exercises on Solving Equations - Exercises - Page 149: 20



Work Step by Step

Let $u=x^{-1}$ $u^2=x^{-2}$ Using the representations above, the given equation becomes: $$-u^2+2u=1$$ Add $u^2$ and subtract $2$ to both sides of the equation to obtain: $$-u^2+2u+u^2-2u=1+u^2-2u \\0=u^2-2u+1$$ Factor the trinomial to obtain: $$0=(u-1)(u-1)$$ Use the Zero-Factor Property by equating each factor to zero to obtain: $$u-1=0 \text{ or } u-1=0$$ Solve each equation to obtain: $$u=1$$ Replacing $u$ with $x^{-1}$ gives: $$u=1 \\x^{-1} = 1$$ Use the rule $a^{-m} = \dfrac{1}{a^m}$, then cross-multiply to obtain: $$\dfrac{1}{x} = 1 \\x(1) = 1 \\x=1$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.