Dễ thấy: \(\left\{{}\begin{matrix}\left|x+1\right|\ge0\\\left|x+2\right|\ge0\\.................\\\left|x+2008\right|\ge0\end{matrix}\right.\)\(\forall x\)
\(\Rightarrow VT=\left|x+1\right|+\left|x+2\right|+...+\left|x+2008\right|\ge0\forall x\)
\(\Rightarrow VP\ge0\forall x\Rightarrow2009x\ge0\Rightarrow x\ge0\)
Vậy \(pt\Leftrightarrow\left(x+1\right)+\left(x+2\right)+...+\left(x+2008\right)=2009x\)
\(\Leftrightarrow\left(x+x+...+x\right)+\left(1+2+...+2008\right)=2009x\)
\(\Leftrightarrow2008x+2017036=2009x\)
\(\Leftrightarrow2009x-2008x=2017036\Leftrightarrow x=2017036\)
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