Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - Summary Exercises on Solving Equations - Exercises: 13

Answer

$\left\{-2, 2, -i, i\right\}$

Work Step by Step

Let $u=x^2 \\u^2=x^4$ The given equation becomes: $u^2-3u-4=0$ Factor the trinomial to obtain: $(u-4)(u+1)=0$ Use the Zero-Factor Property by equating each factor to zero to obtain: $u-4=0$ or $u+1=0$ Solve each equation: $u=4$ or $u=-1$ Replace $u$ with $x^2$ to obtain: $x^2=4$ or $x^2=-1$ Take the square root of both sides to obtain (note that $\sqrt{-1}=i$): $x=\pm \sqrt{4}$ or $x=\pm \sqrt{-1}$ $x = \pm 2$ or $x = \pm i$ Therefore, the solution set is $\left\{-2, 2, -i, i\right\}$.
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