a,Ta có: \(2A=4x^2+4xy+2y^2-4x+4y+4\)
\(=4x^2+2x\left(y-2\right)+\left(y-2\right)^2+y^2+8y+16-20\)
\(=\left(2x+y-2\right)^2+\left(y+4\right)^2-20\)
Vì \(\left\{{}\begin{matrix}\left(2x+y-2\right)^2\ge0\\\left(y+4\right)^2\ge0\end{matrix}\right.\) \(\Rightarrow2A\ge-20\Rightarrow A\ge-10\)
Dấu ''='' xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-4\end{matrix}\right.\)
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c,Ta có:\(4C=4x^2+4xy+4y^2-12x-12y\)
\(=4x^2+2.2x\left(y-3\right)+\left(y-3\right)^2-\left(y-3\right)^2+4y^2-12y\)
\(=\left(2x+y-3\right)^2+3\left(y^2-2y+1\right)-12\)
\(=\left(2x+y-3\right)^2+3\left(y-1\right)^2-12\)
Vì \(\left\{{}\begin{matrix}\left(2x+y-3\right)^2\ge0\\3\left(y-1\right)^2\ge0\end{matrix}\right.\) \(\Rightarrow4C\ge-12\Rightarrow C\ge-3\)
Dấu ''='' xảy ra \(\Leftrightarrow x=y=1\)
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a,Ta có:\(B=x^4-x^3y+y^4-xy^3+x^2y^2-8xy+16+184\)
\(=x\left(x^3-y^3\right)-y\left(x^3-y^3\right)+\left(xy-4\right)^2+184\)
\(=\left(x-y\right)^2\left(x^2+xy+y^2\right)+\left(xy-4\right)^2+184\)
\(=\left(x-y\right)^2\left[\left(x+\dfrac{1}{2}y\right)^2+\dfrac{3y^2}{4}\right]+\left(xy-4\right)^2+184\)
Vì \(\left\{{}\begin{matrix}\left(x-y\right)^2\ge0\\\left[\left(x+\dfrac{1}{2}y\right)^2+\dfrac{3y^2}{4}\right]\ge0\\\left(xy-4\right)^2\ge0\end{matrix}\right.\) \(\Rightarrow B\ge184\)
Dấu ''='' xảy ra \(\Leftrightarrow x=y=2\)
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