\(x^2-2x+1< 9\)
\(\Leftrightarrow\left(x-1\right)^2< 3^2=\left(-3\right)^2\)
\(\Rightarrow x-1< 3\) hoặc \(x-1< -3\)
Nếu x-1<3
\(\Leftrightarrow x< 4\)
Nếu x-1<-3
\(\Leftrightarrow x< -2\)
Ta có
\(x^2-2x+1< 9\Leftrightarrow\left(x-1\right)^2< 9\Leftrightarrow\left(x-1\right)^2-9< 0\Leftrightarrow\left(x-1-3\right)\left(x-1+3\right)< 0\Leftrightarrow\left(x+2\right)\left(x-4\right)< 0\)
\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x+2< 0\\x-4>0\end{matrix}\right.\\\left\{{}\begin{matrix}x+2>0\\x-4< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< -2\\x>4\end{matrix}\right.\\\left\{{}\begin{matrix}x>-2\\x< 4\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow-2< x< 4\)
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