Question

\(|x-6|>|x^2-5x+9|\)

Answer 1

\(\left|x-6\right|>\left|x^2-5x+9\right|\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x^2-5x+9>0\\x-6>x^2-5x+9\end{matrix}\right.\\\left\{{}\begin{matrix}x^2-5x+9< 0\\x-6< -x^2+5x-9\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x^2-5x+9>0\\x^2-6x+15< 0\left(VN\right)\end{matrix}\right.\\\left[{}\begin{matrix}x^2-5x+9< 0\left(VN\right)\\x^2-4x+3< 0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\) BPT VN