Question

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

Em cảm ơn ạ !!!!

Answer 1

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

\(\Rightarrow\left(2x+y\right)\left(x^2+xy+y^2\right)=3\left(x^3+2y^3\right)\)

\(\Rightarrow x^3-3x^2y-3xy^2+5y^3=0\)

\(\Rightarrow\left(x-y\right)\left(x^2-2xy-5y^2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=y\\x=\left(1+\sqrt{6}\right)y\\x=\left(1-\sqrt{6}\right)y\end{matrix}\right.\)

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