Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 9 - Section 9.1 - Solving Quadratic Equations by the Square Root Property - Exercise Set: 15

Answer

$x=\pm\dfrac{\sqrt{6}}{3}$

Work Step by Step

Using the properties of equality, the given equation, $ 3x^2-2=0 ,$ is equivalent to \begin{array}{l}\require{cancel} 3x^2=2 \\\\ x^2=\dfrac{2}{3} .\end{array} Taking the square root of both sides, then the solutions of the given equation are \begin{array}{l}\require{cancel} x=\pm\sqrt{\dfrac{2}{3}} \\\\ x=\pm\sqrt{\dfrac{2}{3}\cdot\dfrac{3}{3}} \\\\ x=\pm\sqrt{\dfrac{6}{(3)^2}} \\\\ x=\pm\dfrac{\sqrt{6}}{\sqrt{(3)^2}} \\\\ x=\pm\dfrac{\sqrt{6}}{3} .\end{array}
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