b) 4x² + y² + 4x-2y=-2. d) 2x² + y²-2xy-2x-4y=-13.

b) `4x^2 + y^2 + 4x - 2y = -2`

`<=> 4x^2 + y^2 + 4x - 2y + 2 = 0`

`<=> (4x^2 + 4x + 1) + (y^2 - 2y + 1) = 0`

`<=> (2x + 1)^2 + (y - 1)^2 = 0`

Ta có : 

`(2x + 1)^2 >= 0 ; (y - 1)^2 >= 0`

`=> (2x + 1)^2 + (y - 1)^2 >= 0`

Dấu "=" xảy ra khi : 

`{(2x + 1 = 0),(y - 1 = 0):} <=> {(2x = -1),(y = 1):}`

`<=> {(x = (-1)/2),(y = 1):}`

Vậy `x = (-1)/2 ; y = 1`

b) `2x^2 + y^2 - 2xy - 2x - 4y = -13`

`<=> 2x^2 + y^2 - 2xy - 2x - 4y + 13 = 0`

`<=> y^2 - 2xy - 4y + (x^2 + 4x + 4) + 2x^2 - 2x - x^2 - 4x +9= 0`

`<=> y^2 - 2y(x + 2) + (x + 2) + x^2 - 6x + 9 = 0`

`<=> (y - x - 2)^2 + (x - 3)^2 = 0`

Ta có : `(y - x - 2)^2 >= 0 ; (x - 2)^2 >= 0`

`=> (y - x - 2)^2 + (x - 3)^2 >= 0`

Dấu "=" xảy ra khi : 

`{(y - x - 2=0),(x -3=0):} <=> {(y - x - 2 = 0),(x = 3):}`

`<=> {(y = 5),(x = 3):}`

Vậy `x = 3 ; y = 5`