Question

Tìm x biết :

\(\left|x-1\right|+\left|x-2\right|+\left|x-3\right|=4\left(x-4\right)\)

Answer 1

Ta thấy:\(\begin{cases}\left|x-1\right|\ge0\\\left|x-2\right|\ge0\\\left|x-3\right|\ge0\end{cases}\)

\(\Rightarrow\left|x-1\right|+\left|x-2\right|+\left|x-3\right|\ge0\)

\(\Rightarrow VT\ge0\Rightarrow VP\ge0\)

\(\Rightarrow4\left(x-4\right)\ge0\Rightarrow x-4\ge0\Rightarrow x\ge4\)

\(\Rightarrow\left(x-1\right)+\left(x-2\right)+\left(x-3\right)=4\left(x-4\right)\)

\(\Rightarrow3x-6=4x-16\)

\(\Rightarrow x=10\) (thỏa mãn)

Vậy \(x=10\)