若x、y、z满足(y+z)/x=(z+x)/y=(x+y)/z=k,求k的值.

Question

若x、y、z满足(y+z)/x=(z+x)/y=(x+y)/z=k,求k的值.

Answer 1

由已知,可得y+x=kx,z+x=ky,x+y=kz三式相加得2(x+y+z)=k(x+y+z)所以当x+y+z不等于0时k=2当x+y+z=0,y+x=-x,得k=-1