Precalculus (6th Edition)

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

Chapter 1 - Equations and Inequalities - Chapter 1 Test Prep - Review Exercises: 62

Answer

$\color{blue}{\left\{-\frac{\sqrt2}{2}, 0, \frac{\sqrt2}{2}\right\}}$

Work Step by Step

Factor out the GCF $x^2$ to obtain: $$x^2(1-2x^2)=0$$ Use the Zero-Factor Property by equating each factor to zero to obtain: $x^2=0$ or $1-2x^2=0$ Solve each equation to obtain: $x^2=0 \\x=\pm \sqrt0 \\x=0$ or $1-2x^2=0 \\1=2x^2 \\\frac{1}{2}=x^2 \\\pm\sqrt{\frac{1}{2}}= \\\pm \sqrt{\frac{1\cdot2}{2\cdot2}}=x \\\pm \frac{\sqrt2}{2}=x$ Thus, the solution set is $\color{blue}{\left\{-\frac{\sqrt2}{2}, 0, \frac{\sqrt2}{2}\right\}}$.
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