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: 19


$x=\pm 3$ or $x=\pm 2\sqrt{2}$

Work Step by Step

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