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 - Connecting: The Concepts - Exercises - Page 712: 8


$t=\displaystyle \frac{\sqrt{11}}{2}$ or $t=-\displaystyle \frac{\sqrt{11}}{2}$

Work Step by Step

$ 4t^{2}=11\qquad$...divide both sides with $4$. $ t^{2}=\displaystyle \frac{11}{4}\qquad$...use the principle of square roots: For any real number $k$ , if $x^{2}=k$ , then $x=\sqrt{k}$ or $x=-\sqrt{k}$ $ t=\pm\sqrt{\frac{11}{4}}\qquad$...apply the quotient rule of square roots:$\displaystyle \sqrt{\frac{a}{b}=}\frac{\sqrt{a}}{\sqrt{b}}$ $ t=\displaystyle \pm\frac{\sqrt{11}}{\sqrt{4}}\qquad$...simplify. $ t=\displaystyle \pm\frac{\sqrt{11}}{2}\qquad$...the symbol $\pm$ indicates two solutions. $t=\displaystyle \frac{\sqrt{11}}{2}$ or $t=-\displaystyle \frac{\sqrt{11}}{2}$
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