解方程:1/x(x+1)+1/(x+2)(x+4)+.+1/(x+8)(x+10)=5/24
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![解方程:1/x(x+1)+1/(x+2)(x+4)+.+1/(x+8)(x+10)=5/24](/uploads/image/z/5254701-69-1.jpg?t=%E8%A7%A3%E6%96%B9%E7%A8%8B%EF%BC%9A1%2Fx%EF%BC%88x%2B1%EF%BC%89%2B1%2F%EF%BC%88x%2B2%EF%BC%89%EF%BC%88x%2B4%EF%BC%89%2B.%2B1%2F%EF%BC%88x%2B8%EF%BC%89%EF%BC%88x%2B10%EF%BC%89%3D5%2F24)
解方程:1/x(x+1)+1/(x+2)(x+4)+.+1/(x+8)(x+10)=5/24
解方程:1/x(x+1)+1/(x+2)(x+4)+.+1/(x+8)(x+10)=5/24
解方程:1/x(x+1)+1/(x+2)(x+4)+.+1/(x+8)(x+10)=5/24
原方程可化为:
(1/2)[1/x-1/(x+1)]+(1/2)[1/(x+2)-1/(x+4)]+…+(1/2)[1/(x+8)-1/(x+10)]=5/24
1/x-1/(x+10)=5/12
12(x+10)-12x=5x(x+10)
x²+10x-24=0
(x-2)(x+12)=0
x=2或x=-12