$\\$
`c,`
`A = -4x^2 - 12x`
`-> A = -4 [x^2 + 3x]`
`-> A = -4 [x^2 + 2 . 3/2x + 9/4 - 9/4]`
`-> A = -4 [x^2 + 2 . 3/2x + (3/2)^2 - 9/4]`
`-> A = -4 (x+3/2)^2 + 9`
Với mọi `x` có : `(x+3/2)^2 ≥ 0`
`-> -4 (x+3/2)^2 ≤ 0∀x`
`-> -4 (x+3/2)^2 + 9≤9∀x`
`-> A≤9∀x`
Dấu "`=`" xảy ra khi :
`↔ (x+3/2)^2=0`
`↔x+3/2=0`
`↔x=(-3)/2`
Vậy `min A=9 ↔x=(-3)/2`
$\\$
`d,`
`A = 7 - x^2 - y^2 - 2 (x+y)`
`-> A = -x^2 - y^2 - 2x - 2y + 7`
`-> A = [-x^2 - 2x -1 ] + [-y^2 - 2y- 1] + 9`
`-> A =-[x^2 + 2x . 1 + 1^2] - [y^2 + 2y . 1 + 1^2] + 9`
`-> A = - (x+1)^2 - (y+1)^2 + 9`
Với mọi `x,y` có : `(x+1)^2 ≥ 0, (y+1)^2 ≥ 0`
`-> - (x+1)^2 ≤0∀x, - (y+1)^2 ≤0∀y`
`->- (x+1)^2 - (y+1)^2 ≤0∀x,y`
`-> - (x+1)^2 - (y+1)^2 + 9≤9∀x,y`
`-> A ≤9∀x,y`
Dấu "`=`" xảy ra khi :
`↔ (x+1)^2=0, (y+1)^2=0`
`↔x+1=0,y+1=0`
`↔x=y=-1`
Vậy `max A=9 ↔x=y=-1`
$\\$
`e,`
`A = 3 - 4x - x^2`
`-> A = [-x^2 - 4x -4] + 7`
`-> A = - [x^2 + 2 . 2x + 2^2] + 7`
`-> A =- (x+2)^2 + 7`
Với mọi `x` có : `(x+2)^2 ≥ 0`
`-> - (x+2)^2 ≤0∀x`
`-> - (x+2)^2 + 7 ≤7∀x`
`-> A≤7∀x`
Dấu "`=`" xảy ra khi :
`↔ (x+2)^2=0`
`↔x+2=0`
`↔x=-2`
Vậy `max A=7 ↔x=-2`
$\\$
`k,`
`A = -4x^2 +4x+3`
`-> A = - [4x^2 -4x - 3]`
`-> A = -[ (2x)^2 - 2 . 2x . 1 + 1^2 - 4]`
`-> A = - (2x - 1)^2 + 4`
Với mọi `x` có : `(2x-1)^2 ≥ 0`
`-> - (2x-1)^2 ≤0∀x`
`-> - (2x-1)^2 + 4≤4∀x`
`-> A≤4∀x`
Dấu "`=`" xảy ra khi :
`↔ (2x-1)^2=0`
`↔2x-1=0`
`↔2x=1`
`↔x=1/2`
Vậy `max A=4 ↔x=1/2`
