Question

\(\left\{{}\begin{matrix}x^3-6x=8y^3-10y\\x^2-4=2\left(1-4y^2\right)\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}x^3-8y^3=6x-10y\\6=x^2+8y^2\end{matrix}\right.\)

Nhân vế với vế:

\(6\left(x^3-8y^3\right)=\left(6x-10y\right)\left(x^2+8y^2\right)\)

\(\Leftrightarrow y\left(5x^2-24xy+16y^2\right)=0\)

\(\Leftrightarrow y\left(x-4y\right)\left(5x-4y\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}y=0\\x=4y\\x=\dfrac{4y}{5}\end{matrix}\right.\)

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