Vì : \(\left|x+2017\right|\ge0\forall x\)
\(\left|y-2017\right|\ge0\forall y\)
\(\Rightarrow\left|x+2017\right|+\left|y-2017\right|\ge0\)
Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x+2017=0\\y-2017=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-2017\\y=2017\end{matrix}\right.\)
Vậy x = -2017 ; y = 2017
b, \(\left|2x-1\right|=\left|x+8\right|\)
\(\Rightarrow\left[{}\begin{matrix}2x-1=x+8\\2x-1=-\left(x+8\right)\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}2x-x=8+1\\2x+x=-8+1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=9\\3x=-7\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=9\\x=\dfrac{-7}{3}\end{matrix}\right.\)
Vậy x = 9
c, \(\left|3x-2\right|-\left|x+14\right|=0\Rightarrow\left|3x-2\right|=\left|x+14\right|\)
\(\Rightarrow\left[{}\begin{matrix}3x-2=x+14\\3x-2=-\left(x+14\right)\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}3x-x=14+2\\3x+x=-14+2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=16\\4x=-12\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=8\\x=-3\end{matrix}\right.\)
Vậy ...
Làm 1 câu thôi nha bạn,mỏi tay lắm:
\(\left|x+2017\right|+\left|y-2017\right|=0\)
\(\left|x+2017\right|\ge0\)
\(\left|x-2017\right|\ge0\)
Dấu "=" xảy ra khi:
\(\left|x+2017\right|=0\Rightarrow x+2017=0\Rightarrow x=-2017\)
\(\left|y-2017\right|=0\Rightarrow y-2017=0\Rightarrow y=2017\)
