Có tôi đây:
\(x^2-2xy+2y^2-2x+6y+5=0\)
\(\Leftrightarrow\left(x^2+y^2+1-2xy-2x+2y\right)+\left(y^2+4y+4\right)=0\)
\(\Leftrightarrow\left(-x+y+1\right)^2+\left(y+2\right)^2=0\)
\(\Leftrightarrow\left\{\begin{matrix}-x+y+1=0\\y+2=0\end{matrix}\right.\Leftrightarrow\left\{\begin{matrix}-x+y+1=0\\y=-2\end{matrix}\right.\Leftrightarrow\left\{\begin{matrix}-x-2+1=0\\y=-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{\begin{matrix}x=-1\\y=-2\end{matrix}\right.\)
Thay vào P:
\(P=\frac{3x^2y-1}{4xy}=\frac{3\left(-1\right)^2\left(-2\right)-1}{4\left(-1\right)\left(-2\right)}=\frac{-7}{8}\)
Vậy \(P=\frac{-7}{8}\)
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