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: 45


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

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: $(n-1)^{2}=8$ Step 2: $n-1=\pm \sqrt {8}$ Step 3: $n-1=\pm \sqrt {4\times2}$ Step 4: $n-1=\pm \sqrt {2^{2}\times2}$ Step 5: $n-1=\pm 2\sqrt {2}$ Step 6: $n-1=+ 2\sqrt {2}$ or $n-1=-2 \sqrt {2}$ Step 7: $n=1+2\sqrt 2$ or $n=1-2\sqrt 2$ The solution set is {$1-2\sqrt 2,1+2\sqrt 2$}.
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