⒈已知x/(y+z)=y/(x+z)=z(x+y)=k,则k的值为多少?分类讨论的题、2种

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⒈已知x/(y+z)=y/(x+z)=z(x+y)=k,则k的值为多少?分类讨论的题、2种

⒈已知x/(y+z)=y/(x+z)=z(x+y)=k,则k的值为多少?分类讨论的题、2种
⒈已知x/(y+z)=y/(x+z)=z(x+y)=k,则k的值为多少?
分类讨论的题、2种

⒈已知x/(y+z)=y/(x+z)=z(x+y)=k,则k的值为多少?分类讨论的题、2种
因为x/(y+z)=y/(x+z)=z/(x+y)=k
所以x=k(y+z)
y=k(x+z)
z=k(x+y)
以上三式相加得:x+y+z=k(y+z)+k(x+z)+k(x+y)
x+y+z=k(2x+2y+2z)
x+y+z=2k(x+y+z)
分类讨论:当x+y+z不等于0时以上左右等式可以同时消去x+y+z
则2k=1
k=1/2
当x+y+z等于零时即x+y+z=0
x+y=-z
带入z/(x+y)=k中得z/-z=k
k=-1
综上所述,当x+y+z不等于零时 k=1/2
当x+y+z=0时 k=-1