Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises - Page 148: 56

Answer

The equation has no solutions.

Work Step by Step

Square both sides $(\sqrt{x+5}+2)^{2}=(\sqrt{x-1})^{2}$ $ x+4\sqrt{x+5}+9=x-1\qquad$ ...Add $-x-9$ to both sides $4\sqrt{x+5}=-10 \qquad$ ... Square both sides $16(x+5)=100$ $16x+80=100 \qquad$ ... Subtract 80 from both sides $16x+80-80=100-80$ $ 16x=20\qquad$ ...Divide both sides by 16 $x=\displaystyle \frac{5}{4}$ Verify Solution: LHS: $\displaystyle \sqrt{\left(\frac{5}{4}\right)+5}+2=\frac{9}{2}$ RHS: $\displaystyle \sqrt{\left(\frac{5}{4}\right)-1}=\frac{1}{2}$ $x=\displaystyle \frac{5}{4}$ is not a solution. The equation has no solutions.
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