Question

Tìm x, y thỏa mãn phương trình \(x^2y^4-16xy^3+68y^2-4xy+x^2=0\)

Answer 1

\(\Leftrightarrow\left(x^2y^4-16xy^3+64y^2\right)+\left(4y^2-4xy+x^2\right)=0\)

\(\Leftrightarrow\left(xy^2-8y\right)^2+\left(2y-x\right)^2=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}xy^2-8y=0\\2y-x=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}xy^2-8y=0\\x=2y\end{matrix}\right.\)

\(\Rightarrow2y.y^2-8y=0\)

\(\Leftrightarrow2y\left(y^2-4\right)=0\Rightarrow\left[{}\begin{matrix}y=0\Rightarrow x=0\\y=2\Rightarrow x=4\\y=-2\Rightarrow x=-4\end{matrix}\right.\)