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