`(x+y)^2+4xy≤8`
`⇔4xy+4xy≤8`
`⇔xy≤1`
mặt khác :
`1/(x+1)+1/(y+1)≤(2)/(1+\sqrt(xy))`
`P=1/(x+1)+1/(y+1)+2020xy≤(2)/(1+\sqrt(xy))+2020xy`
`⇔P≤(2)/(1+\sqrt(xy))+xy+2019`
`⇔P≤(2)/(1+\sqrt(xy))+(\sqrt(xy))^2+2019`
`⇒P≤(2)/(1+\sqrt(xy))+(\sqrt(xy))^2-2+2021`
`⇔P≤((xy+2\sqrt(xy))(\sqrt(xy)-1))/(\sqrt(xy)+1)+2021`
`⇒P≤2021`
`"="` xẩy ra khi :
`x=y=1`