HPT \(\Leftrightarrow\left\{{}\begin{matrix}\left(x-y\right)^2=1\\\left(x-y\right)^3+3xy\left(x-y\right)=2xy+3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x-y=1\\x-y=-1\end{matrix}\right.\\\left(x-y\right)^3+3xy\left(x-y\right)=2xy+3\end{matrix}\right.\).
+) Nếu x - y = 1: Khi đó 1 + 3xy = 2xy + 3
\(\Leftrightarrow xy=2\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=2\\y=1\end{matrix}\right.\\\left[{}\begin{matrix}x=-1\\y=-2\end{matrix}\right.\end{matrix}\right.\).
+) Nếu x - y = -1: Khi đó -1 - 3xy = 2xy + 3
\(\Leftrightarrow5xy=-4\Leftrightarrow xy=-\frac{4}{5}\)
\(\left\{{}\begin{matrix}\left[{}\begin{matrix}x=\frac{-1}{5}\\y=\frac{4}{5}\end{matrix}\right.\\\left[{}\begin{matrix}x=\frac{-4}{5}\\y=\frac{1}{5}\end{matrix}\right.\end{matrix}\right.\).
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