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: 39

Answer

$x=-1$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given radical equation, $ \sqrt[3]{x^2+5x+1}=\sqrt[3]{x^2+4x} ,$ raise both sides of the equation to the third power. Then use properties of equality to isolate and solve the variable. Finally, do checking of the solution/s with the original equation. $\bf{\text{Solution Details:}}$ Raising both sides of the equation to the third power results to \begin{array}{l}\require{cancel} \left(\sqrt[3]{x^2+5x+1}\right)^3=\left(\sqrt[3]{x^2+4x}\right)^3 \\\\ x^2+5x+1=x^2+4x .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} (x^2-x^2)+(5x-4x)=-1 \\\\ x=-1 .\end{array} Upon checking, $ x=-1 $ satisfies the original equation.
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