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解方程:1/x(x+2)+1/(x+2)(x+4)+……+1/(x+8)(x+10)=5/24(x+10)
题目详情
解方程:1/x(x+2)+1/(x+2)(x+4)+……+1/(x+8)(x+10)=5/24(x+10)
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答案和解析
1/x(x+2)+1/(x+2)(x+4)+……+1/(x+8)(x+10)=5/24(x+10)
1/2*[1/x-1/(x+2)]+1/2*[1/(x+2)-1/(x+4)]+.+1/2*[1/(x+8)-1/(x+10)]=5/24(x+10)
1/2*[1/x-1/(x+2)+1/(x+2)-1/(x+4)+.+1/(x+8)-1/(x+10)]=5/24(x+10)
1/2*[1/x-1/(x+10)]=5/24(x+10)
1/2*[(x+10-x)/x(x+10)]=5/24(x+10)
1/2*[10/x(x+10)]=5/24(x+10)
5/x(x+10)=5/24(x+10)
5/x=5/24
x=24
经检验x=24是方程的解
1/2*[1/x-1/(x+2)]+1/2*[1/(x+2)-1/(x+4)]+.+1/2*[1/(x+8)-1/(x+10)]=5/24(x+10)
1/2*[1/x-1/(x+2)+1/(x+2)-1/(x+4)+.+1/(x+8)-1/(x+10)]=5/24(x+10)
1/2*[1/x-1/(x+10)]=5/24(x+10)
1/2*[(x+10-x)/x(x+10)]=5/24(x+10)
1/2*[10/x(x+10)]=5/24(x+10)
5/x(x+10)=5/24(x+10)
5/x=5/24
x=24
经检验x=24是方程的解
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