\(\left|x-2\right|=3x+2\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=3x+2\\x-2=-\left(3x+2\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=0\end{matrix}\right.\)
\(\left|x-2\right|=3x+2\\\Leftrightarrow \left[{}\begin{matrix}x-2=3x+2\\-\left(x-2\right)=3x+2\end{matrix}\right.\\\Leftrightarrow\left[{}\begin{matrix}-2x=4\\-4x=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\x=0\end{matrix}\right. \)
\(\left|x-2\right|=3x+2\left(1\right)\)
*) Nếu \(x-2\ge0\)
\(\Leftrightarrow x\ge2\)
PT \(\left(1\right)\) có : \(x-2=3x+2\)
\(\Leftrightarrow x=-2\)( Ko thỏa mãn )
*) Nếu \(x-2< 0\)
\(\Leftrightarrow x< 2\)
PT \(\left(1\right)\)có : \(x-2=-3x-2\)
\(\Leftrightarrow x=0\)( Thỏa mãn)
Vậy pt có 1 nghiệm duy nhất là \(x=0\)
\(\left|x-2\right|=3x+2\)
<=> \(\left[{}\begin{matrix}x-2=3x+2\left(x\ge2\right)\\2-x=3x+2\left(x< 2\right)\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}2x=-4\left(x\ge2\right)\\4x=0\left(x< 2\right)\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}x=-2\left(x\ge2\right)\left(loại\right)\\x=0\left(x< 2\right)\left(tm\right)\end{matrix}\right.\)
Vậy nghiệm của phương trình trên là \(S=\left\{0\right\}\)
Chúc bạn học tốt
Ta có: \(\left|x-2\right|=3x+2\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=3x+2\left(x\ge2\right)\\-x+2=3x+2\left(x< 2\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3x=2+2\\-x-3x=2-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-2x=4\\-4x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\left(loại\right)\\x=0\left(nhận\right)\end{matrix}\right.\)
Vậy: S={0}