x - y = -658 y = 658 + x (1)
thế (1) vào xy = 1983, ta được:
x.(658 + x) = 1983
+ 658x - 1983 = 0
- 3x + 661x - 1983 = 0
( - 3x) + (661x - 1983) = 0
x(x - 3) + 661(x - 3) = 0
(x - 3)(x + 661) = 0
\(\left\{{}\begin{matrix}xy=1983\\x-y=-658\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}xy=1983\\\left(x-y\right)^2=432964\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}xy=1983\\x^2-2xy+y^2=432964\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}xy=1983\\x^2+y^2=432964-2\cdot1983=428998\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}xy=1983\\x^2+2xy+y^2=428998+2\cdot1983\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}xy=1983\\\left(x+y\right)^2=432964\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x+y=-658\\x+y=658\end{matrix}\right.\)
\(\text{+) Xét }x+y=-658\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-658+\left(-658\right)}{2}=-658\\y=\dfrac{-658-\left(-658\right)}{2}=0\end{matrix}\right.\)
\(\text{+) Xét }x+y=658\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{658+\left(-658\right)}{2}=0\\y=\dfrac{658-\left(-658\right)}{2}=658\end{matrix}\right.\)
Vậy nghiệm của hệ phương trình là \(x;y=\left\{-658;0\right\};\left\{0;658\right\}\)
