设X,Y为实数,且满足（X-1)^3+1998(x-1)=-1;(Y-1)^3+1998(Y-1)=1求X+Y的值

Question

设X,Y为实数,且满足（X-1)^3+1998(x-1)=-1;(Y-1)^3+1998(Y-1)=1
求X+Y的值

Answer 1

(x-1)^3+1998(x-1)=-1
(y-1)^3+1998(y-1)=1
相加得(x-1)^3+1998(x-1)+(y-1)^3+1998(y-1)=0
[(x-1)^3+(y-1)^3]+[1998(x-1)+1998(y-1)]=0
(x-1+y-1)[(x-1)^2-(x-1)(y-1)+(y-1)^2]+1998*(x-1+y-1)=0
(x+y-2)(x^2+y^2-xy-x-y+1999)=0
故x+y=2或x^2+y^2-xy-x-y+1999=0