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: 46


{$-1-2\sqrt 3,-1+2\sqrt 3$}

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: $(n+1)^{2}=12$ Step 2: $n+1=\pm \sqrt {12}$ Step 3: $n+1=\pm \sqrt {4\times3}$ Step 4: $n+1=\pm \sqrt {2^{2}\times3}$ Step 5: $n+1=\pm 2\sqrt {3}$ Step 6: $n+1=+ 2\sqrt {3}$ or $n+1=-2 \sqrt {3}$ Step 7: $n=-1+2\sqrt 3$ or $n=-1-2\sqrt 3$ The solution set is {$-1-2\sqrt 3,-1+2\sqrt 3$}.
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