Question

Tìm x : \(\left|x+2016\right|+\left|x+2017\right|+\left|x+2018\right|=10x\)

Answer 1

Dễ thấy: \(\left\{{}\begin{matrix}\left|x+2016\right|\ge0\\\left|x+2017\right|\ge0\\\left|x+2018\right|\ge0\end{matrix}\right.\)\(\forall x\)

\(\Rightarrow\left|x+2016\right|+\left|x+2017\right|+\left|x+2018\right|\ge0\forall x\)

\(\Rightarrow VT\ge0\Rightarrow VP\ge0\Rightarrow10x\ge0\Rightarrow x\ge10\)

\(pt\Leftrightarrow\left(x+2016\right)+\left(x+2017\right)+\left(x+2018\right)=10x\)

\(\Leftrightarrow3x+6051=10x\)

\(\Leftrightarrow6051=7x\Rightarrow x=\dfrac{6051}{7}\)