Bài `5:`

`A = x + y + z - (x^2 + 2y^2 + 4z^2)`

`A = -x^2 + x - 2y^2 + y - 4z^2 + z`

`A = -(x^2 - x + 1/4) - 2(y^2 - y/2 + 1/16) - 4(z^2 - z/4 + 1/64) + 1/4 + 1/8 + 1/16`

`A = -(x - 1/2)^2 - 2(y - 1/4)^2 - 4(z - 1/8)^2 + 7/16`

Vì  `-(x - 1/2)^2 <= 0 AA x`

`-2(y - 1/4)^2 <= 0 AA y `

`-4(z - 1/8)^2 <= 0 AA z`

`to A <= 7/16`

Dấu "`=`" xảy ra khi:

`{(x - 1/2 = 0),(y - 1/4 = 0),(z - 1/8 = 0):} to {(x = 1/2),(y = 1/4),(z = 1/8):}`

Vậy `max A = 7/16` khi `x = 1/2, y = 1/4, z = 1/8.`

Bài `6:`

`A = x^2 + 2y^2 + 2xy + 2x - 4y + 2013`

`A = (x^2 + 2xy + y^2) + 2(x + y) + 1 + (y^2 - 6y + 9) + 2003`

`A = [(x + y)^2 + 2(x + y) + 1] + (y^2 - 6y + 9) + 2003`

`A = (x + y + 1)^2 + (y - 3)^2 + 2003`

Vì ` (x + y + 1)^2 >= 0 AA x, y `

`(y - 3)^2 >= 0 AA y`

`to A >= 2003`

Dấu "`=`" xảy ra khi`:`

`{(x + y + 1 = 0),(y - 3 = 0):} to {(y = 3),(x = -4):}`

Vậy `min A = 2003` khi `x = -4, y = 3.`