Question

Answer 1

\(\left|3-x\right|\le2\)

\(\Leftrightarrow\left(3-x\right)^2\le4\)

\(\Leftrightarrow9-6x+x^2\le4\)

\(\Leftrightarrow x^2-6x+5\le0\)

\(\Leftrightarrow x^2-x-5x+5\le0\)

\(\Leftrightarrow x\left(x-1\right)-5\left(x-1\right)\le0\)

\(\Leftrightarrow\left(x-5\right)\left(x-1\right)\le0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-5\ge0\\x-1\le0\end{matrix}\right.\\\left\{{}\begin{matrix}x-5\le0\\x-1\ge0\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\)\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge5\\x\le1\end{matrix}\right.\\\left\{{}\begin{matrix}x\le5\\x\ge1\end{matrix}\right.\end{matrix}\right.\)

Thấy TH2 thỏa mãn.

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