解方程: 1⼀x(x+1)+1⼀(x+2)(x+4)+....+1⼀(x+8)(x+10)=5⼀24

2024-11-25 12:28:18
推荐回答(1个)
回答1:

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