Question

giải phương trình  \(_{\left|x-1\right|+\left|x-2\right|=3}\)

 

Answer 1

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

\(\Leftrightarrow\left[{}\begin{matrix}-\left(x-1\right)-\left(x-2\right)=3\\\left(x-1\right)-\left(x-2\right)=3\\\left(x-1\right)+\left(x-2\right)=3\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}-2x=0\\0x=2\\2x=6\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)

Vậy phương trính có hai nghiệm là \(x=0\) và \(x=3\)