Question

Cho x²-2xy+2y²-2x+6y+5=0 tính A=\(\frac{3x^2y-1}{4xy}\)

Answer 1

\(x^2-2xy+2y^2-2x+6y+5=0\)

\(\Leftrightarrow\left(x^2-2xy+y^2\right)+\left(-2x+2y\right)+1+\left(y^2+4y+4\right)=0\)

\(\Leftrightarrow\left(x-y\right)^2-2\left(x-y\right)+1+\left(y+2\right)^2=0\)

\(\Leftrightarrow\left(x-y-1\right)^2+\left(y+2\right)^2=0\)

\(\Leftrightarrow\left\{\begin{matrix}x-y-1=0\\y+2=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{\begin{matrix}x=-1\\y=-2\end{matrix}\right.\)

\(\Rightarrow A=\frac{3x^2y-1}{4xy}=\frac{3.\left(-1\right)^2.\left(-2\right)-1}{4.\left(-1\right).\left(-2\right)}=-\frac{7}{8}\)