|x-2|=2-x
=>x-2=-(2-x) hoặc 2-x
Xét x-2=-(2-x)
=>x-2=x-2
luôn đúng với mọi x thuộc Z
Xét x-2=2-x
=>2x=4
=>x=2
\(\left|x-2\right|=2-x\)
\(\Rightarrow x-2=2-x\)
\(\Rightarrow x+x=2+2\)
\(\Rightarrow2x=4\)
\(\Rightarrow x=2\)
Vì \(\left|x-2\right|\ge0\)
\(\Rightarrow2-x\ge0\)
\(\Rightarrow x\le2\)
\(\Rightarrow\left|x-2\right|=-\left(x-2\right)\)
\(\Rightarrow-\left(x-2\right)=2-x\)
\(\Rightarrow2-x=2-x\)
\(\Rightarrow x\in N\)
Mà x\(\ge\)2
\(\Rightarrow x\in\left\{2;3;4;5;6;7;8;9;.........\right\}\)
Vì \(\left|x-2\right|\ge0\\ =>2-x\ge0\\ =>x\le2\\ =>\left|x+2\right|=-\left(x-2\right)\\ =>-\left(x-2\right)=2-x\\ =>2+x=2-x< =>x\in N\)
Mà : \(x\ge2\\ =>x\in\left\{2;3;4;5;......\right\}\)
\(\left|x-2\right|=2-x\) khi \(\begin{cases}x-2=0\\2-x=0\end{cases}\)
Từ đó suy ra x=2
