College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 1 - Equations and Inequalities - Concept and Vocabulary Check - Page 178: 5


Consider the equation $$\sqrt{x+2}=3-\sqrt{x-1}$$ Squaring the left side and simplifying results in $x+2$ Squaring the right side and simplifying results in $x-6\sqrt{x-1}+8$

Work Step by Step

The equation given is $$\sqrt{x+2}=3-\sqrt{x-1}$$ Squaring the left side results in the elimination of the square root, so the first answer is: $(\sqrt{x+2})^{2}=x+2$ The right side is a binomial, squaring it and simplifying produces the following expression: $(3-\sqrt{x-1})^{2}=9-(2)(3)(\sqrt{x-1})+(\sqrt{x-1})^{2}=...$ $...=9-6\sqrt{x-1}+x-1=...$ $...=x-6\sqrt{x-1}+8$
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