Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 2 - Linear and Quadratic Functions - Section 2.8 Equations and Inequalities Involving the Absolute Value Function - 2.8 Assess Your Understanding - Page 182: 34


$x=-4$ or $x=4$

Work Step by Step

Using the definition of the absolute value, we have $$\displaystyle |x^2-16|=0 \\\Longrightarrow x^2-16=0\\ \Longrightarrow x^2=16 \\\Longrightarrow x=\pm\sqrt{16} \\\Longrightarrow x=\pm4 $$ Thus, we have: $x=4,$ or $x=-4$
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