Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Review - Page 469: 122

Answer

$x=16$

Work Step by Step

Raising both sides to the second power of the given equation, $ \sqrt[]{x+9}=2+\sqrt[]{x-7} ,$ then the solution/s is/are \begin{array}{l}\require{cancel} x+9=(2+\sqrt[]{x-7})^2 \\\\ x+9=(2)^2+2(2)(\sqrt[]{x-7})+(\sqrt[]{x-7})^2 \\\\ x+9=4+4\sqrt[]{x-7}+x-7 \\\\ (x-x)+(9-4+7)=4\sqrt[]{x-7} \\\\ 12=4\sqrt[]{x-7} \\\\ \dfrac{12}{4}=\dfrac{4\sqrt[]{x-7}}{4} \\\\ 3=\sqrt[]{x-7} .\end{array} Squaring both sides again, then, \begin{array}{l}\require{cancel} 9=x-7 \\\\ 9+7=x \\\\ 16=x \\\\ x=16 .\end{array} Upon checking, $ x=16 $ satisfies the original equation.
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