`A = x^2 - 2x + 5 `
`= x^2 - 2x + 1 + 4`
`= (x-1)^2 + 4`
Do `(x-1)^2 = 0 `
`=> (x-1)^2 + 4 >= 4`
Dấu = có khi:
`x - 1 = 0`
`<=> x = 1`
Vậy ....
``
`B = x^2 - x + 1`
`= x^2 - x + 1/4 + 3/4`
`= (x - 1/2)^2 + 3/4`
Do `(x - 1/2)^2 >=0`
`=> (x - 1/2)^2 + 3/4 >= 3/4`
Dấu = có khi:
`x - 1/2 = 0`
`<=> x = 1/2`
Vậy ....
`D = x^2 + 5y^2 - 4xy + 4y + 3`
`= x^2 - 4xy + 4y^2 + y^2 + 4y + 4 - 1`
`= (x - 2y)^2 + (y + 2)^2 - 1`
Do `{((x - 2y)^2 >=0),((y + 2)^2 >=0):}`
`=> (x - 2y)^2 + (y + 2)^2 >=0`
`=> (x - 2y)^2 + (y + 2)^2 - 1 >= -1`
Dấu = có khi:
`{(y + 2 = 0),(x - 2y = 0):}`
`<=> {(y =-2),(x= -4):}`
Vậy ...
