\(\Leftrightarrow x\left(x+y\right)+2022\left(x+y\right)+x+2023=0\)
\(\Leftrightarrow\left(x+y\right)\left(x+2022\right)+x+2022+1=0\)
\(\Leftrightarrow\left(x+2022\right)\left(x+y+1\right)=-1\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+2022=1\\x+y+1=-1\end{matrix}\right.\\\left\{{}\begin{matrix}x+2022=-1\\x+y+1=1\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=-2021\\y=2019\end{matrix}\right.\\\left\{{}\begin{matrix}x=-2023\\y=2023\end{matrix}\right.\end{matrix}\right.\)
\(x^2\)+xy+2023x+2022y+2023=0
\(=\)\(x^2\)\(+\)\(xy\)\(+\)\(x\)\(+\)\(2022x\)\(+\)\(2022y\)\(+2022\)\(+1\)
\(=\)\(x\left(x+y+1\right)\)\(+\)\(2022\left(x+y+1\right)\)\(+1\)
\(\Leftrightarrow\)\(\left(x+2022\right)\left(x+y+1\right)\)\(=\)\(-1\)
\(\Leftrightarrow\)\(x+2022=1\) và \(x+y+1=-1\) hay \(x+2022=-1\) và \(x+y+1=1\)
\(\Leftrightarrow x,y=\left\{-2021;2019\right\};\left\{-2023;2023\right\}\)
x(x+y+1)+2022(x+y+1)=0
=>(x+2022)(x+y+1)=0
=>x=0-2022=-2022
=>y=0+2022-1=2021
\(Ta\) \(có\): \(x^2+xy+2023x+2022y+2023=0\)
\(x\left(x+y\right)2022\left(x+y\right)+x+2023=0\)
\(\left(x+y\right)\left(x+2022\right)+x+2022+1=0\)
\(\left(x+2022\right)\left(x+y+1\right)=-1\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+2022=1\\x+y+1=-1\end{matrix}\right.\\\left\{{}\begin{matrix}x+2022=-1\\x+y+1=1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=-2021\\y=2019\end{matrix}\right.\\\left\{{}\begin{matrix}x=-2023\\y=2023\end{matrix}\right.\end{matrix}\right.\)
x^2 + xy + 2023x + 2022y + 2023=0
x(x + y) + 2022(x + y) + x + 2023 = 0
(x+y)(x+2022) + (x+2022) + 1 = 0
(x+2022)(x+y+1)=-1
=>x+2022=-1;x+y+1=1
hoặc x+2022=1;x+y+1=-1
=>x=-2023;y=2023
hoặc x=-2021;y=2019