Giải:

a) \(x^2-4x+3>0\)

\(\Leftrightarrow x^2-4x+4-1>0\)

\(\Leftrightarrow\left(x-4\right)^2-1>0\)

\(\Leftrightarrow\left(x-3\right)\left(x-5\right)>0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-3>0\\x-5>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-3< 0\\x-5< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>3\\x>5\end{matrix}\right.\\\left\{{}\begin{matrix}x< 3\\x< 5\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>5\\x< 3\end{matrix}\right.\)

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b) \(x^2-4x< 0\)

\(\Leftrightarrow x\left(x-4\right)< 0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\\x-4>0\end{matrix}\right.\\\left\{{}\begin{matrix}x>0\\x-4< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\\x>4\end{matrix}\right.\\\left\{{}\begin{matrix}x>0\\x< 4\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\in\varnothing\\0< x< 4\end{matrix}\right.\)

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