Đặt `A =(x+2)^2 - (2x-1)^2`
` = (x^2 + 2 . x . 2 + 2^2) - [ (2x)^2 - 2 . 2x . 1 + 1^2]`
` = (x^2 + 4x + 4) - (4x^2 - 4x + 1)`
` = x^2 + 4x + 4 - 4x^2 + 4x - 1`
` = -3x^2 + 8x + 3`
` = -3 . (x^2 - 8/3x - 1)`
` = -3 . (x^2 - 2 . x . 4/3 + 16/9) + 25/3`
` = -3 . (x - 4/3)^2 + 25/3`
`\forall x` ta có :
`(x-4/3)^2 \ge 0`
`=> -3 . (x-4/3)^2 \le 0`
`=> -3 . (x-4/3)^2 + 25/3 \le 25/3`
`=> A \le 25/3`
Dấu `=` xảy ra `<=> x - 4/3 = 0`
`<=> x = 4/3`
Vậy `Max_A = 25/3 <=> x = 4/3`
