`#Sad`
`a)`
`C= x^2+x-2`
`= (x^2+x+1/4)-9/4`
`= (x+1/2)^2-9/4`
`\text{Vì}` `(x+1/2)^2 >= 0` `AA x`
`⇒ (x+1/2)^2-9/4 >= -9/4`
`\text{Dấu "=" xảy ra:}`
`⇔ (x+1/2)^2 = 0`
`⇔ x+1/2 = 0`
`⇔ x = -(1)/(2)`
`\text{Vậy MinC}` `=-(9)/(4)` `⇔ x=-(1)/(2)`
`b)`
`D= x^2+y^2+x-6y+5`
`= (x^2+x+1/4)+(y^2-6y+9)-(17)/4`
`= (x+1/2)^2+(y-3)^2-(17)/4`
`\text{Vì}` `(x+1/2)^2+(y-3)^2 >= 0` `AA x; y`
`⇒ (x+1/2)^2+(y-3)^2-(17)/(4) >= -(17)/4`
`\text{Dấu "=" xảy ra:}`
`⇔` `{((x+1/2)^2=0),((y-3)^2=0):}`
`⇔` `{(x+1/2=0),(y-3=0):}`
`⇔` `{(x=-(1)/(2)),(y=3):}`
`\text{Vậy MinD}` `=-(17)/4` `⇔ x=-(1)/(2); y=3`
`c)`
`E= x^2+10y^2-6xy-10y+26`
`= (x^2-6xy+9y^2)+(y^2-10y+25)+1`
`= (x-3y)^2+(y-5)^2+1`
`\text{Vì}` `(x-3y)^2+(y-5)^2 >= 0` `AA x; y`
`⇒ (x-3y)^2+(y-5)^2+1 >= 1`
`\text{Dấu "=" xảy ra:}`
`⇔` `{((x-3y)^2=0),((y-5)^2=0):}`
`⇔` `{(x-3y=0),(y=5):}`
`⇔` `{(x-3. 5=0),(y=5):}`
`⇔` `{(x=15),(y=5):}`
`\text{Vậy MinE}` `=1` `⇔ x=15; y=5`
