已知实数x,y,z满足:x/(x+1)=y/(y+2)=z/(z+3)=(x+y+z)/3,则x+y+z=

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已知实数x,y,z满足:x/(x+1)=y/(y+2)=z/(z+3)=(x+y+z)/3,则x+y+z=
已知实数x,y,z满足:
x/(x+1)=y/(y+2)=z/(z+3)=(x+y+z)/3,则x+y+z=

已知实数x,y,z满足:x/(x+1)=y/(y+2)=z/(z+3)=(x+y+z)/3,则x+y+z=
x/(x+1)=y/(y+2)=z/(z+3)=(x+y+z)/3,则x+y+z=∴(x+1)/x=(y+2)/y=(z+3)/z=3/(x+y+z)
∴[(x+1)+(y+2)+(z+3)]/(x+y+z)=3/(x+y+z)
(x+y+z+6)/(x+y+z)=3/(x+y+z)
x+y+z+6=3
∴x+y+z=-3

当x=y=z=0时,等式成立,此时x+y+z=0
当x,y,z均不为0时(显然x,y,z不可能部分为0,否则等式一定不可能成立)
由x/(x+1)=y/(y+2)=z/(z+3)知:(x+1)/x=(y+2)/y=(z+3)/z
即1/x=2/y=3/z
令:x=k,y=2k,z=3k
则有(x+y+z)/3=2k
且k/(K+1)=2k
解得:k=1
所以有x+y+z=6k=6
望采纳

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