2x^2 + 3y^2 + 4xy - 8x - 2y + 18

= 2x^2 + 4xy - 8x +3y^2 - 2y + 18

=2( x^2 + 2xy -4x ) + 3y^2 - 2y +18

=2( x^2 + 2x( y - 2)) + 3y^2 - 2y + 18

=2(x + y - 2)^2 +3y^2 -2y +18 - 2(y - 2)^2

=2(x +y -2)^2 +3y^2 -2y +18- 2y^2 -8y -8

=2(x +y -2)^2 +y^2 - 10y + 10

Phần còn lại tự làm nhé

Ta có:\(A=2x^2+3y^2+4xy-8x-2y+18\)

\(A=2\left(x^2+2xy+y^2\right)-8\left(x+y\right)+8+y^2+6y+9+1\)

\(A=2\left[\left(x+y\right)^2-4\left(x+y\right)+4\right]+\left(y+3\right)^2+1\)

\(A=2\left(x+y-2\right)^2+\left(y+3\right)^2+1\ge1\)

\(\Rightarrow MINA=1\Leftrightarrow\left\{{}\begin{matrix}x=5\\y=-3\end{matrix}\right.\)

\(=5\left(x^2-\dfrac{4}{5}xy+\dfrac{4}{25}y^2\right)+\dfrac{1}{5}y^2-2y+2023\)

\(=5\left(x-\dfrac{2}{5}y\right)^2+\dfrac{1}{5}\left(y^2-10y+25\right)+2018\)

\(=5\left(x-\dfrac{2}{5}y\right)^2+\dfrac{1}{5}\left(y-5\right)^2+2018>=2018\)

Dấu = xảy ra khi y=5 và x=2/5y=2

\(4B=4x^2+4xy+4y^2-8x-12y+8076\)

= \(\left(2y\right)^2-4y\left(3-x\right)+\left(3-x\right)^2-\left(3-x\right)^2\)

\(+\left(2x\right)^2-8x+8076\)

= \(\left(2y-3+x\right)^2+3x^2-2x+8076\)

đến đây thì dễ rồi

c/ Ta có:\(6a-5b=1\)

\(\Rightarrow5b=6a-1\)

Theo đề thì: \(A=4a^2+\left(6a-1\right)^2=40a^2-12a+1\)

\(=\left(\left(2\sqrt{10}a\right)^2-\frac{2.2.\sqrt{10}.3a}{\sqrt{10}}+\frac{9}{10}\right)+\frac{1}{10}\)

\(=\left(2\sqrt{10}a-\frac{3}{\sqrt{10}}\right)^2+\frac{1}{10}\ge\frac{1}{10}\)

còn câu a,b nữa a ơi :((