Question

[Nguyễn Thị Bích Ngọc]

giai hpt: xy(x-2)(y-2)=4

và x^2+y^2-2(x+y)=4

Giair cho mik cách ngắn vs

Answer 1

[Dũng Lê Trí]

\(xy\left(x-2\right)\left(y-2\right)=4\)

\(\left(x^2-2x\right)y^2+\left(4x-2x^2\right)y=4\)

\(\Rightarrow\left(x^2-2x\right)y^2+\left(4x-2x^2\right)y-4=0\)

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

\(\Rightarrow\left(x^2-2x\right)\left(y^2-2y\right)=4\)

\(\Rightarrow y\left(y-2\right)=\frac{4}{x-\left(x-2\right)}\)

Answer 2

[Dũng Lê Trí]

\(\left(x-2\right)\ne0\)

\(\Leftrightarrow\orbr{y=\frac{x^2-\sqrt{x^4-4x^3+8x^2-8x-2x}}{x^2-2x}}\)