\(=\frac{2x\left(x-2y\right)}{\left(x+2y\right)^2}:\frac{\left(2y-x\right)\left(2y+x\right)}{\left(x-2y\right)^2}:\frac{5xy\left(x-2y\right)}{\left(x+2y\right)^3}\)

Điều kiện: \(x\ne2y;x\ne-2y;x\ne0;y\ne0\)

\(=\frac{2x\left(x-2y\right)}{\left(x+2y\right)^2}:\frac{\left(2y+x\right)}{\left(x-2y\right)}:\frac{5xy\left(x-2y\right)}{\left(x+2y\right)^3}\)

\(=\frac{2x\left(x-2y\right)}{\left(x+2y\right)^2}\times\frac{x-2y}{x+2y}\times\frac{\left(x+2y\right)^3}{5xy\left(x-2y\right)}=\frac{2\left(x-2y\right)}{5y}\)

\(=\dfrac{2x\left(x-2y\right)}{\left(x+2y\right)^2}\cdot\dfrac{\left(x-2y\right)^2}{-\left(x-2y\right)\left(x+2y\right)}:\dfrac{5x^2y-10xy^2}{x^3+6x^2y+12xy^3+8y^3}\)

\(=\dfrac{-2x\left(x-2y\right)^2}{\left(x+2y\right)^3}\cdot\dfrac{\left(x+2y\right)^3}{5xy\left(x-2y\right)}\)

\(=\dfrac{-2x\cdot\left(x-2y\right)}{5xy}=\dfrac{-2\left(x-2y\right)}{5y}\)

a. Ta có: x²+y²-2x+4y+5=0

⇌(x-1)²+(y-2)²=0

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

b. Ta có: 4x²+y²-4x-6y+10=0

⇌ (2x-1)²+(y-3)²=0

\(\Leftrightarrow\left\{{}\begin{matrix}2x-1=0\\y-3=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\\y=3\end{matrix}\right.\)

c.Ta có: 5x²-4xy+y²-4x+4=0

⇌(2x-y)²+(x-2)²=0

\(\Leftrightarrow\left\{{}\begin{matrix}2x-y=0\\x-2=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=4\\x=2\end{matrix}\right.\)

d.Ta có: 2x²-4xy+4y²-10x+25=0

⇌ (x-2y)²+(x-5)²=0

\(\Leftrightarrow\left\{{}\begin{matrix}x-2y=0\\x-5=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{5}{2}\\x=5\end{matrix}\right.\)

Ta có:

\(3x^2-6x+4y^2-4xy+4y+3=0\)

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

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

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

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

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

Vậy ...

nếu bài yêu cầu giải phương trình thì thế này ạ

\(3x^2-6x+4y^2-4xy+4y+3=0\)

\(x^2+4y^2+1-4xy+4y-6x+2x^2-4x+2=0\)

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

mà \(\left(2y-x+1\right)^2,\left(x-1\right)^2\ge0\)

\(\int^{x-1=0}_{2y-x+1=0}\Leftrightarrow\int^{x=1}_{y=0}\)

ai cho mình thêm 4 li-ke cho lên 155 với

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

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

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

Có: \(\left(x-2y\right)^2+\left(x-3\right)^2\ge0\)

Dấu '=' xảy ra khi: \(\hept{\begin{cases}\left(x-2y\right)^2\\\left(x-3\right)^2\end{cases}}\Rightarrow\hept{\begin{cases}x-2y=0\\x-3\end{cases}}\Rightarrow\hept{\begin{cases}x-2y=0\\x=3\end{cases}}\Rightarrow\hept{\begin{cases}3-2y=0\\x=3\end{cases}}\Rightarrow\hept{\begin{cases}y=\frac{3}{2}\\x=3\end{cases}}\)

Vậy: ....