\(A=\left(x^2-xy+\dfrac{1}{4}y^2\right)-2\left(x-\dfrac{1}{2}y\right)+1+\dfrac{11}{4}y^2-11y+11+8\\ A=\left[\left(x-\dfrac{1}{2}y\right)^2-2\left(x-\dfrac{1}{2}y\right)+1\right]+\dfrac{11}{4}\left(y^2-4y+4\right)+8\\ A=\left(x-\dfrac{1}{2}y-1\right)^2+\dfrac{11}{4}\left(y-2\right)^2+8\ge8\)
Dấu \("="\Leftrightarrow\left\{{}\begin{matrix}x-\dfrac{1}{2}y-1=0\\y-2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}y+1=2\\y=2\end{matrix}\right.\)
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