Đáp án`+`Giải thích các bước giải:

 `1, A= -x^2 -4x - y^2 + 2y`

`= -x^2 -4x - 4 - y^2 + 2y -1 +5`

`= -(x + 2)^2 - (y - 1)^2 +5 \le 5 AAx;y \in RR`

Dấu "`=`" xảy ra `<=> {(-(x + 2)^2 =0),(-(y - 1)^2= 0):}`

`<=> {(x =-2),( y = 1):}`

Vậy `MaxA = 5 <=> x =-2;y =1`

`2, B=  1-  5x^2 - y^2 - 4xy + x`

`= (-4x^2 - 4xy - y^2) - x^2 +x - 1/4 + 5/4`

`= - (2x + y)^2 - (x - 1/2)^2 + 5/4 \le 5/4 AAx;y \in RR`

Dấu "`=`" xảy ra `<=> {(-(2x +y)^2= 0),(-(x -1 /2)^2 =0):}`

`<=> {(2x +y  = 0),(x - 1/2=  0):}`

`<=> {(y= -2x),(x = 1/2):}`

`<=> {(y= - 1),(x = 1/2):}`

Vậy `MaxB=  5/4 <=> x = 1/2;y =-1`

`3, C= -x^2 + 2x - y^2 - 4y +6`

`= -x^2 + 2x - 1- y^2 - 4y - 4 + 11`

`= -(x - 1)^2 - (y + 2)^2 +11 \le 11 AAx;y \in RR`

Dấu "`=`" xảy ra`<=> {(-(x - 1)^2= 0),(-(y + 2)^2 =0):}`

`<=> {(x = 1),(y =-2):}`

Vậy `MaxC = 11 <=> x  =1;y= -2`

`4, D= -x^2 - 2x - y^2 + 4y + 6`

`= -x^2 - 2x - 1 - y^2 +4y - 4 + 11`

`= -(x + 1)^2 - (y - 2)^2 +11 \le 11AAx;y \in RR`

Dấu "`=`" xảy ra `<=> {(-(x + 1)^2= 0),(-(y - 2)^2= 0):}`

`<=> {(x =-1),(y = 2):}`

Vậy `MaxD =11 <=> x =-1;y =2`

`***`sharksosad