解方程:(1999-x)^3+(x-1998)^3=1

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/05 21:37:52

(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

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