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: 23


$n=\pm i$ or $n=\pm 2i$

Work Step by Step

$(n^{2}+6)^{2}-7(n^{2}+6)+10=0\qquad$...substitute $n^{2}+6$ for $u$ $ u^{2}-7u+10=0\qquad$... solve with the Quadractic formula. $u=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ $u=\displaystyle \frac{7\pm\sqrt{49-40}}{2}$ $u=\displaystyle \frac{7\pm\sqrt{9}}{2}$ $u=\displaystyle \frac{7\pm 3}{2}$ $u=\displaystyle \frac{7+3}{2}=\frac{10}{2}=5$ or $u=\displaystyle \frac{7-3}{2}=\frac{4}{2}=2$ Bring back $x^{2}=u$. $n^{2}+6=5$ or $n^{2}+6=2$ $n^{2}=-1$ or $n^{2}=-4$ $n=\pm i$ or $n=\pm 2i$
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