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: 14


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

Work Step by Step

$ t^{4}-11t^{2}+18\qquad$...substitute $t^{2}$ for $u$ $ u^{2}-11u+18=0\qquad$... solve with the Quadractic formula. $a=1,\ b=-11,\ c=18$ $ u=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\qquad$... substitute $b$ for $-7,\ a$ for $1$ and $c$ for $18$. $ u=\displaystyle \frac{-(-11)\pm\sqrt{(-11)^{2}-4\cdot(18)\cdot 1}}{2\cdot 1}\qquad$... simplify. $u=\displaystyle \frac{11\pm\sqrt{121-72}}{2}$ $u=\displaystyle \frac{11\pm\sqrt{49}}{2}$ $ u=\displaystyle \frac{11\pm 7}{2}\qquad$... the symbol $\pm$ indicates two solutions. $u=\displaystyle \frac{11+7}{2}=\frac{18}{2}=9$ or $u=\displaystyle \frac{11-7}{2}=\frac{4}{2}=2$ Bring back $t^{2}=u$. $t^{2}=9$ or $t^{2}=2$ $t=\pm 3$ or $t=\pm\sqrt{2}$
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