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
x/(y+z)=y/(x+z)=z/(x+y)=k (y+z)/x=(x+z)/y=(x+y)/z=1/k
(y+z)y=(x+z)x x²+xz=y²+yz
﹛ ﹛ 两式相减x²-z²=yz-xy (x+z)(x-z)+y(x-z)=...
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x/(y+z)=y/(x+z)=z/(x+y)=k (y+z)/x=(x+z)/y=(x+y)/z=1/k
(y+z)y=(x+z)x x²+xz=y²+yz
﹛ ﹛ 两式相减x²-z²=yz-xy (x+z)(x-z)+y(x-z)=0 (x+y+z)(x-z)=0
(x+z)z=(x+y)y z²+xz=xy+y²
得：x+y+z=0(舍去） x-z=0 所以x=z 同理可得y=z k=x/(y=z)=1/2 x/(x+y+z)=1/3
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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 ...
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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
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