Câu hỏi của Lãnh Hàn Thiên Y

Question

a. X×(x-2)<0

b. (X+1)×(x-2)<0

Mọi người giải chi tiết giúp mình nha.

✿✿❑ĐạT̐®ŋɢย❐✿✿ · Accepted Answer

a) $x\cdot\left(x-2\right)< 0$ $\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\x-2>0\end{matrix}\right.\\left\{{}\begin{matrix}x>0\x-2< 0\end{matrix}\right.\end{matrix}\right.$ $\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\x>2\end{matrix}\right.\\left\{{}\begin{matrix}x>0\x< 2\end{matrix}\right.\end{matrix}\right.$ ( Chọn $x>0,x< 2$ ) Vậy : $0< x< 2$Câu trả lời: a) $x\cdot\left(x-2\right)< 0$ $\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\x-2>0\end{matrix}\right.\\left\{{}\begin{matrix}x>0\x-2< 0\end{matrix}\right.\end{matrix}\right.$ $\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\x>2\end{matrix}\right.\\left\{{}\begin{matrix}x>0\x< 2\end{matrix}\right.\end{matrix}\right.$ ( Chọn $x>0,x< 2$ ) Vậy : $0< x< 2$

👁💧👄💧👁 · Answer

a) $x\left(x-2\right)< 0\ \Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\x-2>0\end{matrix}\right.\\left\{{}\begin{matrix}x>0\x-2< 0\end{matrix}\right.\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\x>2\end{matrix}\right.\\left\{{}\begin{matrix}x>0\x< 2\end{matrix}\right.\end{matrix}\right.\Rightarrow0< x< 2$ Vậy 0 < x < 2 b) $\left(x+1\right)\left(x-2\right)< 0\ \Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1>0\x-2< 0\end{matrix}\right.\\left\{{}\begin{matrix}x+1< 0\x-2>0\end{matrix}\right.\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-1\x< 2\end{matrix}\right.\\left\{{}\begin{matrix}x< -1\x>2\end{matrix}\right.\end{matrix}\right.\Rightarrow-1< x< 2$ Vậy -1 < x < 2Câu trả lời: a) $x\left(x-2\right)< 0\ \Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\x-2>0\end{matrix}\right.\\left\{{}\begin{matrix}x>0\x-2< 0\end{matrix}\right.\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\x>2\end{matrix}\right.\\left\{{}\begin{matrix}x>0\x< 2\end{matrix}\right.\end{matrix}\right.\Rightarrow0< x< 2$ Vậy 0 < x < 2 b) $\left(x+1\right)\left(x-2\right)< 0\ \Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1>0\x-2< 0\end{matrix}\right.\\left\{{}\begin{matrix}x+1< 0\x-2>0\end{matrix}\right.\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-1\x< 2\end{matrix}\right.\\left\{{}\begin{matrix}x< -1\x>2\end{matrix}\right.\end{matrix}\right.\Rightarrow-1< x< 2$ Vậy -1 < x < 2

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