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 - Exercise Set 1.6: 38

Answer

The solutions are $x=3$ and $x=-13$

Work Step by Step

$(x+5)^{2/3}=4$ Raise both sides of the equation to $\dfrac{3}{2}$: $[(x+5)^{2/3}]^{3/2}=4^{3/2}$ $x+5=\pm\sqrt{4^{3}}$ Simplify the right side of the equation: $x+5=\pm\sqrt{4^{2}\cdot4}$ $x+5=\pm(4)(2)$ $x+5=\pm8$ Solve for $x$: $x=-5\pm8$ The solutions are: $x=-5+8=3$ $x=-5-8=-13$
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