Question

已知y+z分之x=z+x分之y=x+y分之z,求z分之x+y的值

Answer 1

应该有括号吧?

(y+z)分之x=(z+x)分之y=(x+y)分之z

x/(y+z)=y/(z+x)=z/(x+y)

x/(y+z)=y/(z+x)

xz+x²=y²+yz

x²-y²=yz-xz

(x+y)(x-y)=z(y-x)

当x=y时,由于他们是对称的,所以x=y=z,z分之x+y=(x+y)/z=2

当x≠y时,x+y=-z,(x+y)/z=-1