解方程:1/x(x+2)+1/(x+1)(x+3)+…+1/(x+8)(x+10)=0
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解方程:1/x(x+2)+1/(x+1)(x+3)+…+1/(x+8)(x+10)=0
解方程:1/x(x+2)+1/(x+1)(x+3)+…+1/(x+8)(x+10)=0
解方程:1/x(x+2)+1/(x+1)(x+3)+…+1/(x+8)(x+10)=0
1/2*[1/x-1/(x+2)]+1/2*[1/(x+1)-1/(x+3)]+…+1/2*[1/(x+8)-1/(x+10)]=0
1/2*[1/x-1/(x+2)+1/(x+1)-1/(x+3)+1/(x+2)-1/(x+4)+…+1/(x+8)-1/(x+10)]=0
1/2*[1/x+1/(x+1)-1/(x+9)-1/(x+10)]=0
所以1/x+1/(x+1)-1/(x+9)-1/(x+10)=0
[1/x-1/(x+9)]+[1/(x+1)-1/(x+10)]=0
9/[x(x+9)]+9/[(x+1)(x+10)]=0
9/[x(x+9)]=-9/[(x+1)(x+10)]
所以x(x+9)=-(x+1)(x+10)
x^2+9x=-(x^2+11x+10)
x^2+9x+x^2+11x+10=0
2x^2+20x+10=0
x^2+10x+5=0
x=-5±2√5
打字不易,
楼上是对的,把1/x(x+2)拆成1/2*[1/x-1/(x+2)],
1/(x+1)(x+3)拆成1/2*[1/(x+1)-1/(x+3)]
。。。。。
然后计算就好了