Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Test - Page 751: 22

Answer

$x=2, 3$

Work Step by Step

$x=\sqrt{x-2}+2$ $x-2=\sqrt{x-2}+2-2$ $x-2=\sqrt{x-2}$ $(x-2)^2=(\sqrt{x-2})^2$ $x*x+x*(-2)+x*(-2)+(-2)(-2)=x-2$ $x^2-4x+4=x-2$ $x^2-5x+6=0$ $(x-2)(x-3)=0$ $x-2=0$ $x=2$ $x-3=0$ $x=3$ $x=\sqrt{x-2}+2$ $2=\sqrt{2-2}+2$ $2=\sqrt 0+2$ $2=0+2$ $2=2$ (true) $x=\sqrt{x-2}+2$ $3=\sqrt{3-2}+2$ $3=\sqrt 1+2$ $3=1+2$ (true)
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