Question

已知x分之y+z=y分之x+z=z分之x+y=k，求k的值

Answer 1

x分之y+z=y分之x+z=z分之x+y=k
所以
y+z=kx
x+z=ky
x+y=kz
相加
2(x+y+z)=k(x+y+z)
(x+y+z)(k-2)=0

若k-2=0则k=2
若x+y+z=0则y+z=-x
所以k=(y+z)/x=-x/x=-1

综上
k=2,k=-1

Answer 2

(y+z)/x=(x+z)/y= (x+y)/z = k
=>
y+z=xk (1)
x+z=yk (2)
x+y=zk (3)
(1)+(2)+(3)
2(x+y+z) = (x+y+z)k
k=2