Đáp án:
$\\$
`A = - |x-1| - |x-y+3| +2020`
Với mọi `x,y` có : `|x-1| ≥ 0, |x-y+3| ≥ 0`
`-> - |x-1| ≤0∀x, - |x-y+3| ≤0∀y`
`-> - |x-1| - |x-y+3| ≤0∀x,y`
`-> - |x-1| - |x-y+3| ≤0∀x,y`
`-> - |x-1| - |x-y+3| + 2020 ≤ 2020∀x,y`
`-> A ≤ 2020 ∀x,y`
`-> max A =2020`
Dấu "`=`" xảy ra khi :
`↔ |x-1|=0, |x-y+3|=0`
`↔ x-1=0,x-y+3=0`
`↔x=1,x-y=-3`
`↔x=1, 1-y=-3`
`↔x=1,y=4`
Vậy `max A=2020 ↔ x=1,y=4`