`A=3x^2-15x+1`
`A=3(x^2-5x+1/3)`
`A=3(x^2-2.x. 5/2+25/4-71/2)`
`A=3(x-5/2)^2-71/4>=-71/4`
Dấu = xảy ra khi `x=5/2`
Vậy `A_(min)=-71/4<=>x=5/2`
-----------------------------------
`B=1/4x^2-x-1`
`B=(1/2x)^2-2. 1/2x+1-2`
`B=(1/2x-1)^2-2>=-2`
Dấu = xảy ra khi `1/2x=1<=>x=2`
Vậy `B_(min)=-2<=>x=2`
------------------------------------
`C=1-16x-x^2`
`C=-(x^2+16x-1)`
`C=-(x^2+2.x.8+64-65)`
`C=65-(x+8)^2<=65`
Dấu = xảy ra khi `x+8=0<=>x=-8`
Vậy `C_(max)=65<=>x=-8`
-------------------------------------
`D=x^2+17y^2-8xy+6y+1`
`D=(x^2-8xy+16y^2)+(y^2+6y+9)-8`
`D=(x-4y)^2+(y+3)^2-8>=-8`
Dấu = xảy ra khi `{(x-4y=0),(y+3=0):}<=>{(x=4y),(y=-3):}<=>{(x=-12),(y=-3):}`
Vậy `D_(min)=-8<=>(x;y)=(-12;-3)`
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`E=9x^2+4y^2-6x-4y-1`
`E=(9x^2-6x+1)+(4y^2-4y+1)-3`
`E=(3x-1)^2+(2y-1)^2-3>=-3`
Dấu = xảy ra khi `{(3x-1=0),(2y-1=0):}<=>{(x=1/3),(y=1/2):}`
Vậy `E_(min)=-3<=>(x;y)=(1/3;1/2)`
----------------------------------------
`F=2x^2+9y^2-6xy-6x-12y+2020`
`F=(x^2-6xy+9y^2)+4x-12y+(x^2-10x+25)+1995`
`F=(x-3y)^2+4(x-3y)+4+(x-5)^2+1995`
`F=(x-3y+2)^2+(x-5)^2+1995>=1995`
Dấu = xảy ra khi `{(x-3y=-2),(x=5):}<=>{(x=5),(y=7/3):}`
Vậy `F_(min)=1995<=>(x;y)=(5;7/3)`
-----------------------------------------
`G=x^2+5y^2+4xy-2x-6y+1`
`G=(x^2+4xy+4y^2)-2x-4y+y^2-2y+1`
`G=(x+2y)^2-2(x+2y)+1+(y-1)^2-1`
`G=(x+2y-1)^2+(y-1)^2-1>=-1`
Dấu = xảy ra khi `{(x+2y=1),(y=1):}<=>{(x=-1),(y=1):}`
Vậy `G_(min)=-1<=>(x;y)=(-1;1)`
