Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 3 - Linear and Quadratic Functions - 3.5 Inequalities Involving Quadratic Functions - 3.5 Assess Your Understanding - Page 161: 39


$x=4$. Please refer to the step-by-step part below for the explanation.

Work Step by Step

$(x-4)^2\leq0$, since the square of a real number can only be non-negative, the only solution is when $(x-4)^2=0$. Solve this equation to obtain: \begin{align*}(x-4)^2&=0\\ \sqrt{(x-4)^2}&=\pm \sqrt{0}\\ x-4&=0\\ x&=4\\ \end{align*} Thus, the only solution to the given inequality is $x=4$.
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