Question

Giải hpt \(\left\{{}\begin{matrix}x^2y^2-2x+y^2=0\\2x^2+3=4x-y^3\end{matrix}\right.\)

Thanks các bn!

Answer 1

\(\left\{{}\begin{matrix}x^2y^2-2x+y^2=0\\2x^2+3=4x-y^3\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y^2\left(x^2+1\right)=2x\left(1\right)\\2\left(x^2-2x+1\right)+y^3+1=0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x^2+1\le2x\\2\left(x-1\right)^2+y^3+1=0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\left(x-1\right)^2\le0\\y^3+1\le0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\left(x-1\right)^2=0\left(2\right)\\y\le-1\end{matrix}\right.\)

\(\left(2\right)\Rightarrow x=1\)

Thay x = 1 vào pt (1) ta đc:

\(2y^2=2\Rightarrow y^2=1\Rightarrow y=-1\) ( do \(y\le-1\))