Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.5 - Equations - 1.5 Exercises - Page 57: 125

Answer

$\sqrt (x+a)+\sqrt (x-a)=\sqrt 2\sqrt (x+6)$ If $a=0, x=6$ If $a\gt0, x=\sqrt (36+a^{2})$

Work Step by Step

$\sqrt (x+a)+\sqrt (x-a)=\sqrt 2\sqrt (x+6)$ Domain: $x>or=a$ Square both side: $(\sqrt (x+a)+\sqrt (x-a))^{2}=2(x+6)$ $x+a+2(\sqrt (x+a)\times\sqrt (x-a))+x-a=2x+12$ $2x+2(\sqrt (x+a)\times\sqrt (x-a))=2x+12$ $(\sqrt (x+a)\times\sqrt (x-a))=6$ Square both side: $(x+a)\times(x-a)=36$ $x^{2}-a^{2}=36$ If $a=0, x=6$ or $x=-6 (reject)$ If $a\gt0, x=\sqrt (36+a^{2})$ or $x=-\sqrt (36+a^{2}) (reject)$
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