- 烦人的数学问题X+〔Y〕+{Z}=
- X+〔Y〕+{Z}=-0.9
〔X〕+{Y}+Z=0.2
{X}+Y+〔Z〕=1.3
注:〔〕为该未知数的整数部分
{}为该未知数的小数部分
求10X+10Y+Z的值
- X+[Y]+{Z}=-0.9 (1)
[X]+{Y}+Z=0.2 (2)
{X}+Y+[Z]=1.3 (3)
注意到x=[x]+{x}, y=[y]+{y}, z=[z]+{z}
三式相加,得2(x+y+z)=0.6, x+y+z=0.3 (4)
(4)-(1): y-[y]+z-{z}=1.2, 即{y}+[z]=1.2, {y}=0.2, [z]=1
(4)-(2): {x}+[y]=0.1 {x}=0.1, [y]=0
(4)-(3): [x]+{z}=-1.0 [x]=-1, {z}=0.0
x=[x]+{x}=-1+0.1=-0.9 (小数部分为正)
y=0+0.2=0.2
z=1+0.0
10x+10y+z=-9+2+1=-6
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如果本题是求10x+10y+10z的话,那么求出(4)后,就可得
10x+10y+10z=10(x+y+z)=3