\(A=\left(2x^2-4xy+2y^2\right)+\left(20x-20y\right)+50+\left(2y^2-6y+\dfrac{9}{2}\right)+\dfrac{11}{2}\\ A=2\left[\left(x-y\right)^2+10\left(x-y\right)+25\right]+2\left(y^2-3y+\dfrac{9}{4}\right)+\dfrac{11}{2}\\ A=2\left(x-y+5\right)^2+2\left(y-\dfrac{3}{2}\right)^2+\dfrac{11}{2}\ge\dfrac{11}{2}\\ A_{min}=\dfrac{11}{2}\Leftrightarrow\left\{{}\begin{matrix}x=y-5\\y=\dfrac{3}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{7}{2}\\y=\dfrac{3}{2}\end{matrix}\right.\)
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