tìm giá trj lớn nhất

`\text(Đáp án+Giải thích các bước giải:)`

$\\$`-2x^2-2xy-2y^2+2x-2y-2`

$\\$`=-(x^2+2xy+y^2)-(x^2-2x+1)-(y^2+2y+1)`

$\\$`=-[(x+y)^2+(x-1)^2+(y+1)^2]`

$\\$`\text(Ta có:)`

$\\$`{((x+y)^2>=0),((x-1)^2>=0),((y+1)^2>=0):}`

$\\$`=>(x+y)^2+(x-1)^2+(y+1)^2>=0`

$\\$`=>-[(x+y)^2+(x-1)^2+(y+1)]^2<=0`

$\\$`=>B_(max)=0`

$\\$`\text(Dấu "=" xảy ra khi)`

$\\$`{((x+y)^2>=0),((x-1)^2>=0),((y+1)^2>=0):}`

$\\$`<=>{(x+y=0),(x-1=0),(y+1>=0):}`

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

$\\$`=>x=-y=1`

$\\$Vậy `B_(max)=0` khi `x=-y=1`