Answer
$x=9$
Work Step by Step
$(x-5)^{\frac{3}{2}}=8~~$ (Square both sides):
$[(x-5)^{\frac{3}{2}}]^2=8^2$
$(x-5)^3=64$
$x-5=\sqrt[3] {64}$
$x-5=4$
$x=9$
Check the solution:
$(9-5)^{\frac{3}{2}}=4^{\frac{3}{2}}=(\sqrt 4)^3=2^3=8$
Algebra and Trigonometry 10th Edition
by Larson, Ron
Published by
Cengage Learning
ISBN 10:
9781337271172
ISBN 13:
978-1-33727-117-2
Chapter 1 - 1.6 - Other Types of Equations - 1.6 Exercises - Page 128: 45
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