\(\Leftrightarrow y\left(x^2-2\right)=3x\)
\(\Leftrightarrow y=\dfrac{3x}{x^2-2}\)
\(\left[{}\begin{matrix}x=\pm1\Rightarrow y=\mp3\\x=0\Rightarrow y=0\\\end{matrix}\right.\)
\(x\ne\left\{0,\pm1\right\}\)
\(\left|3x\right|\ge\left|x^2-2\right|\)
\(\Rightarrow\left(I\right)\left\{{}\begin{matrix}x>0\\x^2-2\le3x\end{matrix}\right.\)
\(\Leftrightarrow x^2-3x-2\le0\Rightarrow0< x\le\dfrac{3+\sqrt{17}}{2}..\approx..3,11\)
\(\left[{}\begin{matrix}x=2\Rightarrow y=3\left(nhan\right)\\x=3\Rightarrow y=\dfrac{9}{7}\left(loai\right)\end{matrix}\right.\)
\(\Rightarrow\left(II\right)\left\{{}\begin{matrix}x< 0\\x^2-2\le-3x\end{matrix}\right.\)\(\Leftrightarrow\dfrac{-3-\sqrt{17}}{2}\le x< 0\)
\(\left[{}\begin{matrix}x=-3\Rightarrow y=\dfrac{-9}{7}\left(loai\right)\\x=-2\Rightarrow y=-3\left(nhan\right)\end{matrix}\right.\)
Kết luận:
\(\left(x,y\right)=\left(-1,3\right);\left(1,-3\right);\left(0,0\right);\left(2,3\right);\left(-2,-3\right)\)
\(\)
