Đặt \(A=\left|5-x\right|+\left|x+2\right|\)
Có: \(\left\{{}\begin{matrix}\left|5-x\right|\ge5-x\forall x\\\left|x+2\right|\ge x+2\forall x\end{matrix}\right.\)
\(\Rightarrow\left|5-x\right|+\left|x+2\right|\ge5-x+x+2\forall x\\ \Rightarrow A\ge7\forall x\\ \Rightarrow A_{min}=7\\ "="\Leftrightarrow\left\{{}\begin{matrix}\left|5-x\right|=5-x\\\left|x+2\right|=x+2\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}5-x\ge0\\x+2\ge0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}0\le x\le5\\x\ge-2\end{matrix}\right.\)
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