Question

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

Answer 1

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