1/(X-1)(X-2)+1/(X-2)(X-3)+…+1/(X-5)(X-6)=1/10

来源：百度知道编辑：UC知道时间：2024/06/01 20:48:31

求X的值

1/(X-1)(X-2)+1/(X-2)(X-3)+…+1/(X-5)(X-6)=1/10
[1/(X-2)-1/(X-1)]+[1/(X-3)-1/(X-2)]+……+[1/(X-6)-1/(X-5)]=1/10
1/(X-6)-1/(X-1)=1/10
(X-1-X+6)/(X-6)(X-1)=1/10
5/(X^2-7X+6)=1/10
X^2-7X+6=50
X^2-7X-44=0
(X-11)(X+4)=0
X=11,X=-4
经检验，X=11,X=-4都是方程的根

1/(X-1)(X-2)+1/(X-2)(X-3)+…+1/(X-5)(X-6)
=1/(X-2)-1/(X-1)+1/(X-3)-1/(X-2)+……+1/(X-6)-1/(X-5)
=1/(x-6)-1/(x-1)=1/10
再解得，X=11或-4

1/(x-1)(x-2)=1/(x-2)-1/(x-1)
1/(x-2)(x-3)=1/(x-3)-1/(x-2)
....
左式=1/(x-6)-1/(x-1)=1/10
x=11

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