Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.6 - Complex Numbers - 1.6 Exercises: 62

Answer

$x=0\pm\dfrac{\sqrt{3}}{3}i$

Work Step by Step

$3x^{2}+1=0$ Take the $1$ to the right side: $3x^{2}=-1$ Take the $3$ dividing to the right side of the equation: $x^{2}=-\dfrac{1}{3}$ Take the square root of both sides: $\sqrt{x^{2}}=\sqrt{-\dfrac{1}{3}}$ $x=\pm\sqrt{\dfrac{1}{3}}i=\pm\dfrac{1}{\sqrt{3}}i=\pm\dfrac{\sqrt{3}}{3}i$ The solution is $x=0\pm\dfrac{\sqrt{3}}{3}i$
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