若x,y,z满足x/(y+z)=y/(x+z)=z/(x+y)=k,且x+y+z≠0,求k和x/(x+y+z)
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若x,y,z满足x/(y+z)=y/(x+z)=z/(x+y)=k,且x+y+z≠0,求k和x/(x+y+z)
若x,y,z满足(y+z)/x=(x+z)/y=(x+y)/z=k,且x+y+z≠0,求k和(x+y+z)/x
(y+z)/x=(x+z)/y=(x+y)/z=k
xk=y+z xk+x=x+y+z k+1=(x+y+z)/x
yk=x+z yk+y=x+z k+1=(x+y+z)/y
zk=x+y zk+z=x+y+z k+1=(x+y+z)/z
∵x+y+z≠0
∴x=y=z
∴k+1=3x/x
k=3-1=2
(x+y+z)/x=3x/x=3
(y+z)/x=(x+z)/y=(x+y)/z=k
xk=y+z xk+x=x+y+z k+1=(x+y+z)/x
yk=x+z yk+y=x+z k+1=(x+y+z)/y
zk=x+y zk+z=x+y+z k+1=(x+y+z)/z
∵x+y+z≠0
∴x=y=z
∴k+1=3x/x
k=3-1=2
(x+y+z)/x=3x/x=3
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