引用:
原帖由 老猫 于 2007-11-18 07:19 发表
解方程[3x+1]=2x-0.5
设x=a+b,其中a为整数,0<=b<1
当0<=b<1/3时,[3x+1]=3a+1=2(a+b)-0.5,a=2b-1.5,-3/2<=a<-5/6,得a=-1,b=1/4,x=-3/4
当1/3<=b<2/3时,[3x+1]=3a+2=2(a+b)-0.5,a=2b-2.5,-11/6<=a<-7/6,无解
当2/3<=b<3/3时,[3x+1]=3a+3=2(a+b)-0.5,a=2b-3.5,-13/6<=a<-3/2,得a=-2,b=3/4,x=-5/4
x1=-3/4
x2=-5/4.