College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.6 - Solving Other Types of Equations - 1.6 Exercises - Page 139: 60


The solution is $x=256$

Work Step by Step

$\sqrt{x}-3\sqrt[4]{x}-4=0\hspace{0.7cm} \color{blue}{\text{Given equation}}$ $x^{1/2}-3x^{1/4}-4=0$ $(x^{1/4})^2-3x^{1/4}-4=0$ $W^2-3W-4=0\hspace{3.3cm} \color{blue}{\text{Let } W=x^{1/4}}$ $(W+1)+(W-4)=0\hspace{2.3cm} \color{blue}{\text{Factor}}$ $W+1=0\hspace{0.5cm}or\hspace{0.5cm}W-4=0\hspace{1.3cm} \color{blue}{\text{Zero-Product Property}}$ $W=-1\hspace{1.5cm}W=4\hspace{1.99cm} \color{blue}{\text{Solve}}$ Now change $W$ back into the correspondimg values of $x$ $x^{1/4}=-1\hspace{1.5cm}x^{1/4}=4$ $x=\text{due to -ve sign the solution rejects}\hspace{1.5cm}x=256$ The solution is $x=256$
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