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: 24

Answer

$m=\pm 1$ or $m=\pm 3i$

Work Step by Step

$(m^{2}+7)^{2}-6(m^{2}+7)-16=0\qquad$...substitute $m^{2}+7$ for $u$ $ u^{2}-6u-16=0\qquad$... solve with the Quadratic formula. $u=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ $u=\displaystyle \frac{6\pm\sqrt{36+64}}{2}$ $u=\displaystyle \frac{6\pm\sqrt{100}}{2}$ $u=\displaystyle \frac{6\pm 10}{2}$ $u=\displaystyle \frac{6+10}{2}=\frac{16}{2}=8$ or $u=\displaystyle \frac{6-10}{2}=\frac{-4}{2}=-2$ Bring back $m^{2}+7=u$. $m^{2}+7=8$ or $m^{2}+7=-2$ $m^{2}=1$ or $m^{2}=-9$ $m=\pm 1$ or $m=\pm 3i$
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