Question

\(\left|x+y\right|+\left|2x-y\right|=0\)

Answer 1

Có: \(\left|x+y\right|\ge0;\left|2x-y\right|\ge0\)

Mà theo đề bài: \(\left|x+y\right|+\left|2x-y\right|=0\)

\(\Rightarrow\begin{cases}\left|x+y\right|=0\\\left|2x-y\right|=0\end{cases}\)\(\Rightarrow\begin{cases}x+y=0\\2x-y=0\end{cases}\)

=> (2x - y) + (x + y) = 0 + 0

=> 3x = 0

=> x = 0 : 3 = 0

=> y = 0 - 0 = 0

Vậy x = 0; y = 0

Answer 2

\(\left|x+y\right|+\left|2x-y\right|=0\)

\(\Leftrightarrow\begin{cases}x+y=0\\2x-y=0\end{cases}\)

\(\Leftrightarrow\begin{cases}x=-y\\-2y-y=0\end{cases}\)\(\Leftrightarrow\begin{cases}x=-y\\y=0\end{cases}\)\(\Leftrightarrow x=y=0\)