$\\$
`a,`
`A = (x-5/6)^2 + (xy - 1/4)^4 -85`
Với mọi `x,y` có : `(x-5/6)^2 ≥ 0, (xy-1/4)^4 ≥ 0`
`-> (x-5/6)^2 + (xy-1/4)^4 ≥ 0∀x,y`
`-> (x-5/6)^2 + (xy-1/4)^4 -85 ≥-85∀x,y`
`-> A≥-85∀x,y`
Dấu "`=`" xảy ra khi :
`↔ (x-5/6)^2=0, (xy-1/4)^4=0`
`↔x-5/6=0, xy-1/4=0`
`↔x=5/6, 5/6y=1/4`
`↔ x=5/6, y=3/10`
Vậy `min A=-85 ↔x=5/6,y=3/10`
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`b,`
`B = -5 (3x + 2)^4 + [-(x+2y)^2]^5 +111`
`-> B =-5 (3x+2)^4 - (x+2y)^{10} + 111`
Với mọi `x,y` có : `(3x+2)^4 ≥ 0, (x+2y)^{10} ≥ 0`
`-> -5 (3x+2)^4 ≤0∀x, - (x+2y)^{10} ≤0∀y`
`->- 5 (3x+2)^4 - (x+2y)^{10} ≤0∀x,y`
`-> - 5 (3x+2)^4 - (x+2y)^{10} +111 ≤111∀x,y`
`-> B ≤111∀x,y`
Dấu "`=`" xảy ra khi :
`↔ (3x+2)^4=0, (x+2y)^2=0`
`↔3x+2=0,x+2y=0`
`↔3x=-2, 2y=-x`
`↔ x=(-2)/3, 2y=2/3`
`↔x=(-2)/3, y=1/3`
Vậy `max B=111 ↔x=(-2)/3, y=1/3`