`bb(b o t)`

`bb(1.)`

`A=(2x+1)^2 - (x-2)^2 -15`

`A=4x^2 +4x + 1 - (x^2 - 4x +4) - 15`

`A = 4x^2 + 4x + 1 - x^2 + 4x -4 - 15`

`A=3x^2 + 8x - 18`

`A = 3 (x^2 + 8/3 x ) -18`

`A =3(x^2 + 2 . x . 4/3 + 4^2/3^2 - 4^2/3^2) - 18`

`A=3(x + 4/3)^2 - 16/3 - 18`

`A=3(x+4/3)^2 - 70/3`

Ta có `:`

`(x+4/3)^2 >=0 AA x`

`to A=3(x+4/3)^2 - 70/3 >= -70/3 AA x`

`to Amin = -70/3`

Dấu "`=`" xảy ra khi `:`

`x+4/3 = 0`

`x=-4/3`

Vậy `Amin = -70/3` khi `x=-4/3`

`bb(2.)`

`B=(y+2x)^2 + (x+1)^2 - 11`

Ta có `:`

`(y +2x)^2 >=0 AA x;y`

`(x+1)^2 >=0 AA x`

`to B = (y+2x)^2 + (x+1)^2 -11 >= -11 AA x;y`

`to B min = -11`

Dấu "`=`" xảy ra khi `:`

`{(y +2x=0),(x+1=0):} to {(y =-2x),(x=-1):} to {(y=2),(x=-1):}`

Vậy `Bmin =-11` khi `x=-1 ; y =2.`

`bb(3.)`

`C=(x-2)(x-5) -10`

`C=x^2 - 7x + 10 - 10`

`C=x^2 - 7x `

`C =x^2 - 2 . x . 7/2 + (7/2)^2 - (7/2)^2`

`C=(x-7/2)^2 - 49/4 `

Ta có `:`

`(x-7/2)^2 >=0 AA x `

`to C =(x-7/2)^2 - 49/4 >= -49/4 AA x`

`to C min =-49/4`

Dấu "`=`" xảy ra khi `:`

`x-7/2= 0`

`to x=7/2`

Vậy `C min = 49/4` khi `x=7/2`

`bb(4.)` 

`D=x^2 +3x + 2y^2 - 10y + 10`

`D=x^2 + 2 .x . 3/2 + (3/2)^2 + 2(y^2 - 5y) + 10 - (3/2)^2`

`D=(x+3/2)^2 +2(y^2 - 2 .y . 5/2 + 5^2/2^2 - 5^2/2^2) + 10 - 9/4`

`D=(x+3/2)^2 + 2(y - 5/2)^2 -25/2 + 10 - 9/4`

`D=(x+3/2)^2 +2(y-5/2)^2 - 19/4`

Ta có `:`

`(x+3/2)^2 >=0 AA x`

`(y-5/2)^2 >=0 AA y`

`to D=(x+3/2)^2 +2(y-5/2)^2 - 19/4 >= -19/4 AA x;y`

`to D min =-19/4` 

Dấu "`=`" xảy ra khi `:`

`{(x+3/2=0),(y-5/2=0):} to {(x=-3/2),(y=5/2):}`

Vậy `D min =-19/4` khi `x=-3/2 ; y = 5/2`

`bb(5.)`

`D = x^2 +2x +3y^2 - 18y + 10`

`D = x^2 +2x + 1 + 3(y^2 - 6y ) + 10 - 1`

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

`D=(x+1)^2 +3(y-3)^2 - 27+ 9`

`D=(x+1)^2 +3(y-3)^2 - 18`

Ta có `:`

`(x+1)^2 >=0 AA x`

`(y-3)^2 >=0 AA x`

`to D =(x+1)^2 + 3(y-3)^2 - 18 >= -18 AA x;y`

`to D min = -18`

Dấu "`=`" xảy ra khi `:`

`{(x+1=0),(y-3=0):} to {(x=-1),(y=3):}`

Vậy `D min =-18` khi `x=-1 ; y =3 .`