Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.6 - Solving Equations with Radicals - 7.6 Exercises: 26


no solution

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given radical equation, $ x=\sqrt{x^2-4x-8} ,$ square both sides of the equation and then isolate the variable. Finally, do checking of the solution with the original equation. $\bf{\text{Solution Details:}}$ Squaring both sides of the equation results to \begin{array}{l}\require{cancel} \left( x \right)^2=\left( \sqrt{x^2-4x-8} \right)^2 \\\\ x^2=x^2-4x-8 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} x^2-x^2+4x=-8 \\\\ 4x=-8 \\\\ x=-\dfrac{8}{4} \\\\ x=-2 .\end{array} Upon checking, $ x=-2 $ DOES NOT satisfy the original equation. Hence, there is $\text{ no solution .}$
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