Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 11 - Quadratic Functions and Equations - 11.5 Equations Reducible to Quadratic - 11.5 Exercise Set - Page 731: 21


$x=\pm 2$ or $x=\pm 3i$

Work Step by Step

$ x^{4}+5x^{2}-36=0\qquad$...substitute $x^{2}$ for $u$ $ u^{2}+5u-36=0\qquad$... solve with the Quadractic formula. $u=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ $u=\displaystyle \frac{-5\pm\sqrt{25+144}}{2}$ $u=\displaystyle \frac{-5\pm\sqrt{169}}{2}$ $u=\displaystyle \frac{-5\pm 13}{2}$ $u=\displaystyle \frac{-5+13}{2}=\frac{8}{2}=4$ or $u=\displaystyle \frac{-5-13}{2}=\frac{-18}{2}=-9$ Bring back $x^{2}=u$. $x^{2}=4$ or $x^{2}=-9$ $x=\pm 2$ or $x=\pm 3i$
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