a)  ... = (x^2 -2xy + y^2)+(x^2 -2x+1)+2014=(x-y)^2 + (x-1)^2 +2014 >= 2014 

Đăngt thức xay ra khi x=y=1

\(A=2x^2+y^2+2xy+60+8x+8y\)

    \(=\left(x^2+y^2+2xy\right)+8x+8y+16+y^2+44\)

    \(=\left(x+y\right)^2+2\left(x+y\right).4+16+y^2+44\)

    \(=\left(x+y+4\right)^2+y^2+44\)

Vì \(\hept{\begin{cases}\left(x+y+4\right)^2\ge0\forall x\\y^2\ge0\forall y\end{cases}}\)

\(\Rightarrow A\ge44\)

Dấu = xảy ra \(\Leftrightarrow\hept{\begin{cases}x+y+4=0\\y=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=-4\\y=0\end{cases}}\)

Vậy \(minA=44\Leftrightarrow\hept{\begin{cases}x=-4\\y=0\end{cases}}\)

bạn cũng dc đó

\(A=\dfrac{3x^2-2xy}{x^2+2xy+y^2}=\dfrac{15x^2-10xy}{5\left(x^2+2xy+y^2\right)}=\dfrac{-\left(x^2+2xy+y^2\right)+16x^2-8xy+y^2}{5\left(x^2+2xy+y^2\right)}\)

\(A=-\dfrac{1}{5}+\dfrac{\left(4x-y\right)^2}{5\left(x+y\right)^2}\ge-\dfrac{1}{5}\)

\(A_{min}=-\dfrac{1}{5}\) khi \(4x-y=0\)

Giải PT: \(x^2+3y^2+2xy-8x-16y+23=0\)

\(\Leftrightarrow x^2+y^2+16+2xy-8x-8y+2y^2-8y+7=0\)

\(\Leftrightarrow\left(x+y-4\right)^2+2\left(y^2-4y+4\right)-1=0\)

\(\Leftrightarrow\left(x+y-4\right)^2+2\left(y-2\right)^2-1=0\)

\(\Rightarrow\left(x+y-4\right)^2=-2\left(y-2\right)^2+1\le1\)

Dấu "=" xảy ra khi : \(-2\left(y-2\right)^2=0\Rightarrow y=2\)

\(\Rightarrow\)\(\text{│}x+y-4\text{│}\le1\)

\(\Rightarrow-1\le x+y-4\le1\)

\(\Rightarrow3\le x+y\le5\)

Vậy B_min=3 khi y=2;x=1

       B_max=5 khi y=2;x=3