`a)`
`A = x^2 - 2x + y^2 - 7y + 9`
`A = x^2 - 2x + 1 + y^2 - 2 . y . 7/2 + 49/4 - 17/4`
`A = (x - 1)^2 + (y - 7/2)^2 - 17/4`
`Do (x - 1)^2 + (y - 7/2)^2 ≥ 0`
`⇒ A ≥ -17/4`
`text(Min)` `A = -17/4 khi x = 1 ; y = 7/2`
`b)`
`B = x^2 + 2y^2 - 4x - 8y + 2xy + 13`
`B = x^2 + 2xy + y^2 - 4x - 4y + 4 + y^2 - 4y + 4 + 5`
`B = (x + y)^2 - 4(x + y) + 4 + (y - 2)^2 + 5`
`B = (x + y - 2)^2 + (y - 2)^2 + 5`
`Do (x + y - 2)^2 + (y - 2)^2 ≥ 0`
`⇒ B ≥ 5`
`text(Min)` `B = 5 khi y = 2 ; x = 0`
`c)`
`C = (x - 1)(x + 2)(x + 3)(x + 6)`
`C = (x - 1)(x + 6)(x + 2)(x + 3)`
`C = (x^2 + 5x - 6)(x^2 + 5x + 6)`
`Đặt x^2 + 5x - 6 = a `
`⇒ C = a(a + 12)`
`C = a^2 + 12a`
`C = a^2 + 2 . a . 6 + 36 - 36`
`C = (a + 6)^2 - 36 ≥ -36`
`text(Min)` `C = -36 khi a = -6 ⇔ x = {0 ; -5}`
