Question

tìm x,y,z biết

a) \(\text{x}^{\text{2}}+5\text{y}^{\text{2}}-4xy+6y+9=0 \)

b) \(2\text{x}^{\text{2}}+4\text{y}^{\text{2}}+\text{z}^{\text{2}}-4xy+4\text{y}^{\text{2}}-2x+2z+5=0\)

Answer 1

a) \(x^2+5y^2-4xy+6y+9=0\)

\(\Leftrightarrow\left(x^2-4xy+4y^2\right)+\left(y^2+6y+9\right)=0\)

\(\Leftrightarrow\left(x-2y\right)^2+\left(y+3\right)^2=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-2y=0\\y+3=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=2y=2.\left(-3\right)=-6\\y=-3\end{matrix}\right.\)

Vậy : \(\left(x,y\right)=\left(-6,-3\right)\)