Ta có: \(\left|x+4\right|\ge0\forall x\)
\(\left|y+1\right|\ge0\forall y\)
Do đó: \(\left|x+4\right|+\left|y+1\right|\ge0\forall x,y\)
*Trường hợp 1:
\(\left\{{}\begin{matrix}\left|x+4\right|=0\\\left|y+1\right|=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+4=0\\y+1\in\left\{2;-2\right\}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-4\\y\in\left\{1;-3\right\}\end{matrix}\right.\)
*Trường hợp 2:
\(\left\{{}\begin{matrix}\left|x+4\right|=1\\\left|y+1\right|=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+4\in\left\{1;-1\right\}\\y+1\in\left\{1;-1\right\}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\in\left\{-3;-5\right\}\\y\in\left\{0;-2\right\}\end{matrix}\right.\)
*Trường hợp 3:
\(\left\{{}\begin{matrix}\left|x+4\right|=2\\\left|y+1\right|=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+4\in\left\{2;-2\right\}\\y+1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\in\left\{-2;-6\right\}\\y=-1\end{matrix}\right.\)
Vậy: \(x\in\left\{-2;-3;-4;-5;-6\right\}\)
Lo phòng tránh dịch corona trước đi bạn ơi
|x + 4| + |y + 1| = 2
x + 4 ∈ {0; -1; 1; -2; 2}
Ta có bảng sau :
| x + 4 | 0 | -1 | 1 | -2 | 2 |
| x | -4 | -5 | -3 | -6 | -2 |
➤ Vậy x ∈ {-4; -5; -3; -6; -2}
