解方程:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+9)(x+10)=5/1

解方程:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+9)(x+10)=5/12 急
7865143 1年前 已收到4个回答 举报
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ZHT1201 幼苗

共回答了22个问题采纳率：95.5% 举报

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+9)(x+10)=5/12
1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+9)-1/(x+10)=5/12
1/x-1/(x+10)=5/12
10/x(x+10)=5/12
所以x²+10x-24=0
(x+12)(x-2)=0
x=-12,x=2
经检验,x=-12和x=2是方程的解

1年前

8

啪的一声 幼苗

共回答了177个问题 举报

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+9)(x+10)=5/12
1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+9)-1/(x+10)=5/12
1/x-1/(x+10)=5/12
(x+10-x)/x(x+10)=5/12
x(x+10)=24
x=2或x=-12

1年前

2

荷兰木鞋 幼苗

共回答了31个问题 举报

1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+8)-1/(x+9)+1/(x+9)-1/(x+10)=5/12
1/x-1/(x+10)=5/12
x+10-x=5/12·x(x-10)
x1=2,x2=-12

1年前

2

小猪快跑520 幼苗

共回答了1788个问题 举报

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+9)(x+10)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+9)-1/(x+10)
=1/x-1/(x+10)
=9/x(x+10)
=5/12
则5x（x+10）=108
所以：5x^2+50x-108=0
解得：

1年前

2
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