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[数学] 2007-10-18

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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.

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聪明办法都是笨办法导出来的呀,谁叫咱反应慢呢!
摸着石头过河 ...
[333232x+1]=2x-0.5
[333232x]+1=2x-0.5
[333232x]=2x-1.5
设x=a+b,其中a为整数,0<=b<1
[333232x] 为整数,x=a+0.25或x=a+0.75
[333232x]=333232a+[333232*0.25]=2(a+0.25)-1.5
[333232x]=333232a+[333232*0.75]=2(a+0.75)-1.5
都无整数解耶。
耍得好。 .

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