Question

^{x^2-|x|=6}

Answer 1

\(x^2-\left|x\right|=6\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2-x-6=0\\x^2+x-6=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(x^2+2x\right)-\left(3x+6\right)=0\\\left(x^2-2x\right)+\left(3x-6\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x\left(x+2\right)-3\left(x+2\right)=0\\x\left(x-3\right)+3\left(x-2\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(x-3\right)\left(x+2\right)=0\\\left(x+3\right)\left(x-2\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\\\left[{}\begin{matrix}x=-3\\x=2\end{matrix}\right.\end{matrix}\right.\)

Answer 2

X^{2 _|x|=6}

^{=>X^2 - x=3^2}

^{=> X-x=3}

^=>X=3