Tìm GTNN của biểu thức : a) A= x ² -2xy+6y ² -12x+2y+2021 b) B= x ² +y ² – xy-x+y+1 Hứa cho cthn và vote 5 sao

`a) A=x^2-2xy+6y^2-12x+2y+2021`

`A=(x^2-2xy+y^2)-(12x-12y)+(5y^2-10y+5)+2016`

`A=(x-y)^2-12(x-y)+36+5(y^2-2y+1)+1980`

`A=(x-y-6)^2+5(y-1)^2+1980>=1980`

Dấu = có khi `{(x-y-6=0),(y-1=0):}`

`<=>{(x-1=6),(y=1):}`

`<=> {(x=7),(y=1):}`

Vậy `A_(min)=1980<=> (x;y)=(7;1)`

`b) B=x^2+y^2-xy-x+y+1`

`4B=4x^2+4y^2-4xy-4x+4y+4`

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

`4B=(2x-y)^2-2(2x-y)+1+3y^2+2y+3`

`4B=(2x-y-1)^2+3y^2+2y+3`

`3.4B=3(2x-y-1)^2+9y^2+6y+9`

`12B=3(2x-y-1)^2+(9y^2+6y+1)+8`

`12B=3(2x-y-1)^2+(3y+1)^2+8`

`B=(2x-y-1)^2/4+(3y+1)^2/12+2/3>=2/3`

Dấu = có khi `{(2x-y-1=0),(3y+1=0):}`

`<=> {(2x+1/3=1),(y=-1/3):}`

`<=> {(x=1/3),(y=-1/3):}`

Vậy `B_(min)=2/3 <=> (x;y)=(1/3;-1/3)`