`a)`
`C=x^2+x-2`
`=x^2+x+1/4 -9/4`
`=x^2+2. 1/2 .x +(1/2)^2-9/4`
`=(x+1/2)^2-9/4`
Vì `(x+1/2)^2≥0∀x`
`->(x+1/2)^2-9/4≥-9/4∀x`
`->C≥-9/4`
Dấu `'='` xảy ra `<=>x+1/2=0<=>x=-1/2`
Vậy `C_{min}=-9/4` khi `x=-1/2`
`b)`
`D=x^2+y^2+x-6y+5`
`=x^2+x+1/4 +y^2-6y+9-17/4`
`=[x^2+2. 1/2 . x+(1/2)^2]+(y^2-2.3.y+3^2)-17/4`
`=(x+1/2)^2+(y-3)^2-17/4`
Vì `(x+1/2)^2≥0∀x`
`(y-3)^2≥0∀y`
`->(x+1/2)^2+(y-3)^2≥0∀x;y`
`->(x+1/2)^2+(y-3)^2-17/4≥-17/4∀x;y`
`->D≥-17/4`
Dấu `'='` xảy ra `<=>{(x+1/2=0),(y-3=0):}`
`<=>{(x=-1/2),(y=3):}`
Vậy `D_{min}=-17/4` khi `(x;y)=(-1/2;3)`
`c)`
`E=x^2+10y^2-6xy-10y+26`
`=x^2-6xy+9y^2+y^2-10y+25+1`
`=[x^2-2.x.3y+(3y)^2]+(y^2-2.5y+5^2)+1`
`=(x-3y)^2+(y-5)^2+1`
Vì `(x-3y)^2>=0∀x;y`
`(y-5)^2≥∀y`
`->(x-3y)^2+(y-5)^2≥0∀x;y`
`->(x-3y)^2+(y-5)^2+1≥1∀x;y`
`->E>=1`
Dấu `'='` xảy ra `<=>{(x-3y=0),(y-5=0):}`
`<=>{(x-3.5=0),(y=5):}`
`<=>{(x=15),(y=5):}`
Vậy `E_{min}=1` khi `(x;y)=(15;5)`
