College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.6 - Equations and Inequalities Involving Absolute Value - 1.6 Assess Your Understanding: 29

Answer

The real solution set is {-1,3}.

Work Step by Step

$|x^2-2x|=3$ $x^2-2x=3$ or $x^2-2x=-3$ $x^2-2x-3=0$ or $x^2-2x+3=0$ $(x-3)(x+1)=0$ or $x=\frac{2+\sqrt {4-12}}{2}$ or $x=\frac{2-\sqrt {4-12}}{2}$ $(x-3)=0$ or $(x+1)=0 $ or $x=\frac{2+\sqrt {-8}}{2}$ or $x=\frac{2-\sqrt {-8}}{2}$ $x=3 $ or $x=-1$ or $x=\frac{2+2i\sqrt {2}}{2}=1+i\sqrt 2$ or $x=\frac{2-2i\sqrt {2}}{2}=1-i\sqrt 2$ The real solution set is {-1,3}
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