Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 10 - Quadratic Equations - 10.1 - Quadratic Equations - Problem Set 10.1: 34

Answer

{$-\frac{4\sqrt 3}{3}, \frac{4\sqrt 3}{3}$}

Work Step by Step

Using Property 10.1, which states that for any non-negative real number $a$, $x^{2}=a$ can be written as $x=\pm\sqrt a$, we obtain: Step 1: $3x^{2}=16$ Step 2: $x^{2}=\frac{16}{3}$ Step 3: $x=\pm \sqrt {\frac{16}{3}}$ Step 4: $x=\pm \frac{\sqrt {16}}{\sqrt 3}$ Step 5: $x=\pm \frac{4}{\sqrt 3}$ Step 6: $x=\pm \frac{4}{\sqrt 3}\times\frac{\sqrt 3}{\sqrt 3}$ Step 7: $x=\pm \frac{4\sqrt 3}{(\sqrt 3)^{2}}$ Step 8: $x=\pm \frac{4\sqrt 3}{3}$ The solution set is {$-\frac{4\sqrt 3}{3}, \frac{4\sqrt 3}{3}$}.
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