x y z x+y--- = --- = ---- ----y+Z z+x x+y ,求 z 的值 .求 x+y----z

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x y z x+y--- = --- = ---- ----y+Z z+x x+y ,求 z 的值 .求 x+y----z
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x y z x+y--- = --- = ---- ----y+Z z+x x+y ,求 z 的值 .求 x+y----z
x y z x+y
--- = --- = ---- ----
y+Z z+x x+y ,求 z 的值 .
求 x+y
----
z

x y z x+y--- = --- = ---- ----y+Z z+x x+y ,求 z 的值 .求 x+y----z
x/(y+z)=y/(x+z)=z/(x+y)
当x+y+z=0时,
x+y=-z
(x+y)/z=-z/z=-1
当x+y+z≠0时,
由x/(y+z)=y/(x+z)=z/(x+y)根据等比性质可得
(x+y+z)/(2x+2y+2z)=(x+y)/z=1/2
所以(x+y)/z=1/2
,(x+y)/z