Question

[yencba]

Tim x biet |x+2| - |1-x| = 3

Answer 1

[Phùng Minh Quân]

\(VT=\left|x+2\right|-\left|1-x\right|=\left|x+2\right|-\left|x-1\right|\le\left|x+2-x+1\right|=\left|3\right|=3=VP\)

Dấu "=" xảy ra \(\Leftrightarrow\)\(\left(x+2\right)\left(x-1\right)\ge0\)

TH 1 : \(\hept{\begin{cases}x+2\ge0\\x-1\ge0\end{cases}}\Leftrightarrow\hept{\begin{cases}x\ge-2\\x\ge1\end{cases}\Leftrightarrow x\ge1}\)

TH 2 : \(\hept{\begin{cases}x+2\le0\\x-1\le0\end{cases}\Leftrightarrow\hept{\begin{cases}x\le-2\\x\le1\end{cases}\Leftrightarrow}x\le-2}\)

Vậy \(x\ge1\) hoặc \(x\le-2\)

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