chứng tỏ cái gì

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Dùng định nghĩa hai phân thức bằng nhau chứng tỏ rằng: 

- Chứng Tỏ Rằng J Hả Bạn ??????

\(A=2x^2+9y^2-6xy-6x-12y+2004\)

\(A=\left(3y\right)^2-2\cdot3y\cdot2+2^2+2x^2-6x+2000\)

\(A=\left(3y-2\right)^2+2\left(x^2-2\cdot x\cdot\frac{3}{2}+\left(\frac{3}{2}\right)^2\right)+1997,75\)

\(A=\left(3y-2\right)^2+2\left(x-\frac{3}{2}\right)^2+1997,75\)

\(A\ge1997,75\)

Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}3y-2=0\\x-\frac{3}{2}=0\end{cases}\Leftrightarrow\hept{\begin{cases}y=\frac{2}{3}\\x=\frac{3}{2}\end{cases}}}\)

Vậy,.........

Sửa cho Bonking ( bắt đầu dòng 3 )

\(A=\left(3y-2\right)^2+2\left(x^2-2\cdot x\cdot\frac{3}{2}+\left(\frac{3}{2}\right)^2-\left(\frac{3}{2}\right)^2\right)+2000\)

\(A=\left(3y-2\right)^2+2\left[\left(x-\frac{3}{2}\right)^2-\frac{9}{4}\right]+2000\)

\(A=\left(3y-2\right)^2+2\left(x-\frac{3}{2}\right)^2-\frac{9}{2}+2000\)

\(A=\left(3y-2\right)^2+2\left(x-\frac{3}{2}\right)^2+1995,5\)

\(A\ge1995,5\)

Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}3y-2=0\\x-\frac{3}{2}=0\end{cases}\Leftrightarrow}\hept{\begin{cases}y=\frac{2}{3}\\x=\frac{3}{2}\end{cases}}\)

Vậy,.........

\(\left(a+b\right)^2-4ab\)

\(=a^2+2ab+b^2-4ab\)

\(=a^2-2ab+b^2\)

\(=\left(a-b\right)^2=VT\left(đpcm\right)\)