Precalculus (6th Edition)

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

Chapter 1 - Equations and Inequalities - 1.4 Quadratic Equations - 1.4 Exercises: 35

Answer

$\color{blue}{\left\{\dfrac{3-i\sqrt3}{5}, \dfrac{3+i\sqrt3}{5}\right\}}$.

Work Step by Step

RECALL: If $x^2=a$, then taking the square root of both sides gives $x = \pm \sqrt{a}$. Take the square root of both sides of the given equation to obtain: $\sqrt{(5x-3)^2}=\pm \sqrt{-3} \\5x-3 =\pm \sqrt{-1(3)}$ Since $\sqrt{-1}=i$, then the expression above is equivalent to: $5x-3=\pm i\sqrt{3}$ Add $3$ to both sides: $x =3 \pm i\sqrt{3}$ Divide $5$ to both sides: $x=\dfrac{3\pm i\sqrt3}{5}$ Thus, the solution set is $\color{blue}{\left\{\dfrac{3-i\sqrt3}{5}, \dfrac{3+i\sqrt3}{5}\right\}}$.
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