Question

\(\left\{{}\begin{matrix}x^3-y^3=7\\xy\left(x-y\right)=2\end{matrix}\right.\)

Answer 1

HPT đã cho tương đương với:

\(\left\{{}\begin{matrix}\left(x-y\right)^3+3xy\left(x-y\right)=7\\xy\left(x-y\right)=2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-y\right)^3+3.2=7\\xy\left(x-y\right)=2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-y=1\\xy\left(x-y\right)=2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-y=1\\xy=2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\\\left\{{}\begin{matrix}x=-1\\y=-2\end{matrix}\right.\end{matrix}\right.\)

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