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: 20


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

Work Step by Step

$(x^{2}-2)^{2}-12(x^{2}-2)+20=0\qquad$...substitute $x^{2}-2$ for $u$ $ u^{2}-12u+20=0\qquad$... solve with the Quadratic formula. $u=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ $u=\displaystyle \frac{12\pm\sqrt{144-80}}{2}$ $u=\displaystyle \frac{12\pm\sqrt{64}}{2}$ $u=\displaystyle \frac{12\pm 8}{2}$ $u=\displaystyle \frac{12+8}{2}=\frac{20}{2}=10$ or $u=\displaystyle \frac{12-8}{2}=\frac{4}{2}=2$ Bring back $x^{2}-2=u$. $x^{2}-2=10$ or $x^{2}-2=2$ $x^{2}=12$ or $x^{2}=4$ $x=\pm 2\sqrt{3}$ or $x=\pm 2$
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