z/x+y=x/y+z=y/x+z=k,求k

Question

z/x+y=x/y+z=y/x+z=k,求k

Answer 1

.z/x+y=x/y+z=y/x+z=k
z=k(x+y)
x=k(y+z)
y=k(x+z)
三式相加得到x+y+z=2k(x+y+z)
(1)当x+y+z不=0时有k=1/2
(2)当x+y+z=0时有z=-(x+y),k=z/(x+y)=-1