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: 10

Answer

The solutions are $x=\left\{-2, 2\right\}$.

Work Step by Step

Use the property $a^m = a^n \longrightarrow m=n$ to obtain: $\begin{array}{ccc} &2x^2-3&=&9-x^2 \\&2x^2-3+x^2&=&9-x^2+x^2 \\&3x^2-3&=&9 \\&3x^2-3+3&=&9+3 \\&3x^2&=&12 \\&\dfrac{3x^2}{3} &= &\dfrac{12}{3} \\&x^2&=&4 \\&\sqrt{x^2}&=&\pm\sqrt{4} \\&x&=&\pm2 \end{array}$ Thus, the solutions are $x=\left\{-2, 2\right\}$.
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