(1999-x)^3+(x-1998)^3=1
=[(1999-x)+(x-1998)][(1999-x)^2-(1999-x)(x-1998)+(x-1998)^2]=1
(1999-x)^2-(1999-x)(x-1998)+(x-1998)^2-1=0
(1999-x)^2-(1999-x)(x-1998)+(x-1998-1)(x-1998+1)=0
(1999-x)^2-(1999-x)(x-1998)+(x-1999)(x-1997)=0
(1999-x)^2-(1999-x)(x-1998)-(1999-x)(x-1997)=0
(1999-x)[(1999-x)-(x-1998)-(x-1997)]=0
(1999-x)(1999-x-x+1998-x+1997)=0
(1999-x)(5994-3x)=0
x1=1999
x2=5994/3=1998