Question

If $|x{|}^2-6|x|+9\le 4$, then $x\in$

• A. $[-5,5]-(-1,1)$
• B. $[1,5]$
• C. $[-5,5]$
• D. $[-5,-1]$

Answer 1

The correct option is A $[-5,5]-(-1,1)$

$|x{|}^2-6|x|+9\le 4\Rightarrow (|x|-3{)}^2\le 4\Rightarrow -2\le |x|-3\le 2\Rightarrow 1\le |x|\le 5\Rightarrow x\in [-5,-1]\cup [1,5]$
$\therefore x\in [-5,5]-(-1,1)$