Question

|x|+|y|=1

Answer 1

Ta có: |x|≥0∀x

|y|≥0∀y

Do đó: |x|+|y|≥0∀x,y

mà |x|+|y|=1

nên \(\left\{{}\begin{matrix}\left\{{}\begin{matrix}\left|x\right|=1\\\left|y\right|=0\end{matrix}\right.\\\left\{{}\begin{matrix}\left|x\right|=0\\\left|y\right|=1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}x\in\left\{1;-1\right\}\\y=0\end{matrix}\right.\\\left\{{}\begin{matrix}x=0\\y\in\left\{1;-1\right\}\end{matrix}\right.\end{matrix}\right.\)

Vậy: (x,y)∈{(1;0);(-1;0);(0;1);(0;-1)}