Question

Tìm x,y

\(\left|x-y\right|^{2017}+\left|x+y\right|^{2018}=0\)

Answer 1

+ \(\left\{{}\begin{matrix}\left|x-y\right|^{2017}\ge0\forall x,y\\\left|x+y\right|^{2018}\ge0\forall x,y\end{matrix}\right.\)

\(\Rightarrow\left|x-y\right|^{2017}+\left|x+y\right|^{2018}\ge0\forall x,y\)

Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}\left|x-y\right|^{2017}=0\\\left|x+y\right|^{2018}=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-y=0\\x+y=0\end{matrix}\right.\Leftrightarrow x=y=0\)