解方程:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+9)(x+10)=5/1
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/09/28 21:30:47
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
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/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
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