`A=-x^2-3y^2-2xy+10x+14y-18`
`=(-x^2-2xy+10x)-3y^2+14y-18`
`=-(x^2+2xy-10x)-3y^2+14y-18`
`=-[x^2+2x(y-5)]-3y^2+14y-18`
`=-[x^2+2x(y-5)+(y-5)^2]+(y-5)^2-3y^2+14y-18`
`=-(x+y-5)^2+y^2-10y+25-3y^2+14y-18`
`=-(x+y-5)^2-2y^2+4y+7`
`=-(x+y-5)^2-2y^2+4y-2+9`
`=-(x+y-5)^2-2(y-1)^2+9<=9`
Dấu `=` xảy ra `<=>`$\begin{cases}x+y-5=0\\y-1=0\end{cases}$
`<=>`$\begin{cases}x=4\\y=1\end{cases}$
Vậy `A_{max}=9` đạt được khi `x=4;y=1`
