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: 36

Answer

{$- \frac{7\sqrt 3}{6}, \frac{7\sqrt 3}{6}$}

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: $12n^{2}=49$ Step 2: $n^{2}=\frac{49}{12}$ Step 3: $n=\pm \sqrt {\frac{49}{12}}$ Step 4: $n=\pm \frac{\sqrt {49}}{\sqrt {12}}$ Step 5: $n=\pm \frac{\sqrt {49}}{\sqrt {4\times3}}$ Step 6: $n=\pm \frac{7}{2\sqrt 3}$ Step 7: $n=\pm \frac{7}{2\sqrt 3}\times\frac{2\sqrt 3}{2\sqrt 3}$ Step 8: $n=\pm \frac{14\sqrt 3}{(2\sqrt 3)^{2}}$ Step 9: $n=\pm \frac{14\sqrt 3}{4 \times 3}$ Step 10: $n=\pm \frac{14\sqrt 3}{12}$ Step 11: $n=\pm \frac{7\sqrt 3}{6}$ The solution set is {$- \frac{7\sqrt 3}{6}, \frac{7\sqrt 3}{6}$}.
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