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 \(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-4\end{matrix}\right.\)

Vậy ....

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 \(\Leftrightarrow x=y=1\)

Vậy ...

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 \(\Leftrightarrow x=y=2\)

Vậy ...

Ta có:

D=2x2+3y2+4xy−8x−2y+18C=2x2+3y2+4xy−8x−2y+18

D=2(x2+2xy+y2)+y2−8x−2y+18C=2(x2+2xy+y2)+y2−8x−2y+18

D=2[(x+y)2−4(x+y)+4]+(y2+6y+9)+1C=2[(x+y)2−4(x+y)+4]+(y2+6y+9)+1

D=2(x+y−2)2+(y+3)2+1≥1C=2(x+y−2)2+(y+3)2+1≥1

Dấu "=" xảy ra ⇔x+y=2⇔x+y=2và y=−3y=−3

Hay x = 5 , y = -3

Đc chx bạn