`a)`
`A=x^2-20x+101`
`=x^2-20x+100+1`
`=(x-10)^2+1`
Vì `(x-10)^2>=0∀x`
`=>(x-10)^2+1>=1∀x`
`=>A>=1`
Vậy `A_min=1<=>(x-10)^2=0<=>x=10`
`B=4a^2+4a+2`
`=4a^2+4a+1+1`
`=(2a+1)^2+1`
Vì `(2a+1)^2>=0∀x`
`=>(2a+1)^2+1>=1∀x`
`=>B>=1`
Vậy `B_min=1<=>(2a+1)^2=0<=>a=-1/2`
`c)`
`C=x^2-4xy+5y^2-22y+10x+28`
`=x^2-4xy+4y^2+y^2-20y-2y+10x+25+3`
`=(x^2-4xy+4y^2)+(10x-20y)+(y^2-2y)+28`
`=(x-2y)^2+10(x-2y)+25+(y-1)^2+2`
`=(x-2y+5)^2+(y-1)^2+2`
Vì `{((x-2y+5)^2>=0∀x;y),((y-1)^2>=0∀y):}`
`=>(x-2y+5)^2+(y-1)^2+2>=2∀x;y`
`=>C>=2`
Vậy `C_min=2<=>{((x-2y+5)^2=0),((y-1)^2=0):}<=>{(x=2y-5),(y=1):}<=>{(x=-3),(y=1):}`
