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 - Page 178: 39


The solutions are $x=5$ and $x=-4$

Work Step by Step

$(x^{2}-x-4)^{3/4}-2=6$ Take the $2$ to the right side of the equation: $(x^{2}-x-4)^{3/4}=6+2$ $(x^{2}-x-4)^{3/4}=8$ Raise both sides to $\dfrac{4}{3}$: $[(x^{2}-x-4)^{3/4}]^{4/3}=8^{4/3}$ $x^{2}-x-4=\sqrt[3]{8^{4}}$ Simplify the right side: $x^{2}-x-4=\sqrt[3]{8^{3}\cdot8}$ $x^{2}-x-4=(8)(2)$ $x^{2}-x-4=16$ Take $16$ to the left side and simplify: $x^{2}-x-4-16=0$ $x^{2}-x-20=0$ Solve by factoring: $(x-5)(x+4)=0$ Set both factors equal to $0$ and solve each individual equation for $x$: $x-5=0$ $x=5$ $x+4=0$ $x=-4$ The solutions are $x=5$ and $x=-4$
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