\(\left|x+y\right|+\left|x-2017\right|=0\)
Mà \(\left|x+y\right|+\left|x-2017\right|\ge0\)
\(\Rightarrow\left\{\begin{matrix}x-2017=0\\x+y=0\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=2017\\y=-2017\end{matrix}\right.\)
Vậy \(\left\{\begin{matrix}x=2017\\y=-2017\end{matrix}\right.\)
Vì : \(\left|x+y\right|\ge0\forall x,y\) ; \(\left|x-2017\right|\ge0\forall x\)
\(\Rightarrow\left|x+y\right|+\left|x-2017\right|\ge0\forall x,y\)
Mà : \(\left|x+y\right|+\left|x-2017\right|=0\)
\(\Rightarrow\left|x+y\right|=0\) và \(\left|x-2017\right|=0\)
\(\Rightarrow x-2017=0\Rightarrow x=0+2017=2017\)
\(\Rightarrow\left|x+y\right|=0\Leftrightarrow\left|2017+y\right|=0\Rightarrow2017+y=0\)
\(\Rightarrow y=0-2017=-2017\)
Vậy x = 2017 và y = -2017
