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=

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=
令x/(x+1)=y/(y+2)=z/(z+3)=(x+y+z)/3=m,则
x=(x+1)m,y=(y+2)m,z=(z+3)m,x+y+z=3m
前三式相加得
x+y+z=(x+y+z+6)m
将x+y+z=3m代入得
3m=(3m+6)m
m=(m+2)m
(m+2)m-m=0
m(m+1)=0
m=0或m=-1
所以x+y+z=3m=0或-3

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