Question

Find values of $x$ for which $x^2-\left|x\right|-2\ge 0$

Answer 1

Given: $x^2-|x|-2\ge 0$

To find the value of $x$

Sol: $x^2-|x|-2\ge 0⟹|x{|}^2-|x|-2\ge 0⟹|x{|}^2-2|x|+|x|-2\ge 0⟹|x|(|x|-2)+1(|x|-2)\ge 0⟹(|x|+1)(|x|-2)\ge 0$

$|x|+1$ is always greater than $0$

$\Rightarrow |x|-2\ge 0$

$\therefore x<-2$ or $x>2$