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`H=(-1)/3 x^2 - 5x + 1`
`-> H = (-1)/3 (x^2 + 15x - 3)`
`->H = (-1)/3 (x^2 + 2 . x . 15/2 + 225/4 - 237/4)`
`->H = (-1)/3 (x+15/2)^2 + 79/4 ≤ 79/4 ∀x`
Dấu "`=`" xảy ra khi :
`(x+15/2)^2=0 ↔ x+15/2=0 ↔x=(-15)/2`
Vậy `max H=79/4 ↔x=(-15)/2`
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`L=-3x^2 + 6x - y^2 + 6y - 12`
`->L = (-3x^2 + 6x -3) + (-y^2 + 6y - 9)`
`->L = -3 (x^2 - 2x +1) - (y^2 - 6y + 9)`
`->L=-3 (x-1)^2 - (y-3)^2 ≤0∀x,y`
Dấu "`=`" xảy ra khi :
`(x-1)^2=0, (y-3)^2=0`
`↔x-1=0,y-3=0`
`↔x=1,y=3`
Vậy `max L=0 ↔x=1,y=3`