`x+2y+2/(x+1)`

`=((x+1)/2+2/(x+1))+(x-(x+1)/2)+2y`

`>=2+(x-1)/2+2y`

`=(x+4y+3)/2`

`y+2x+2/(y+1)`

`>=(y+4x+3)/2` (tương tự)

`VT>={(x+4y+3)(y+4x+3)}/4`

`VT>=((4x^2+4y^2)+17xy+15(x+y)+9)/4`

`VT>=(8xy+17xy+15(2sqrt{xy})+9)/4`

`VT>=(25xy+30sqrt{xy}+9)/4`

`VT>=(5sqrt{xy}+3)^2/4`

`VT>=(5+3)^2/4`

`VT>=16` (đpcm)

Dấu `=` xảy ra khi `x=y=1`