Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 8 - Section 8.4 - Equations Quadratic in Form - Exercise Set - Page 637: 69


$x = ±\sqrt[3] \frac{9}{5}$ or $x=±\sqrt[3] {2}i$

Work Step by Step

$5x^6 + x^3 = 18$ Let $u=x^3$ Substitute. $5u^2 + u = 18$ Get the factors. $(5u-9)(u+2)=0$ $5u-9=0$ or $u+2=0$ $u=\frac{9}{5}$ or $u=-2$ Refer to the original substitution to get the value of $x$. $u=x^3$ $\frac{9}{5}=x^3$ or $-2=x^3$ $x = ±\sqrt[3] \frac{9}{5}$ or $x=±\sqrt[3] {-2}$ $x = ±\sqrt[3] \frac{9}{5}$ or $x=±\sqrt[3] {2}i$
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