Question

Giải hộ mình câu này

(x-1)*(3-x)<0

Answer 1

\(\left(x-1\right)\left(3-x\right)< 0\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\\3-x< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\\3-x>0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>1\\x< 3\end{matrix}\right.\\\left\{{}\begin{matrix}x< 1\\x>3\end{matrix}\right.\left(loại\right)}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x>1\\x< 3\end{matrix}\right.\)

Answer 2

\(\left(x-1\right)\left(3-x\right)< 0\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\\3-x< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\\3-x>0\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>1\\x< 3\end{matrix}\right.\\\left\{{}\begin{matrix}x< 1\\x>3\end{matrix}\right.\left(loai\right)\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>1\\x< 3\end{matrix}\right.\)

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