College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 404: 9


The solutions are $x=\left\{-1, 1\right\}$.

Work Step by Step

Use the property $a^m = a^n \longrightarrow m=n$ to obtain: $\begin{array}{ccc} &x^2-1&=&1-x^2 \\&x^2-1+x^2&=&1-x^2+x^2 \\&2x^2-1&=&1 \\&2x^2-1+1&=&1+1 \\&2x^2&=&2 \\&\dfrac{2x^2}{2} &= &\dfrac{2}{2} \\&x^2&=&1 \\&\sqrt{x^2}&=&\pm\sqrt{1} \\&x&=&\pm1 \end{array}$ Thus, the solutions are $x=\left\{-1, 1\right\}$.
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