数学线段之比已知Y+Z分之X=X+Z分之Y=X+Y分之Z,求Z分之X+Y的值?

Question

数学线段之比
已知Y+Z分之X=X+Z分之Y=X+Y分之Z,求Z分之X+Y的值?

Answer 1

y+z分之x=x+z分之y=x+y分之z,即x/(y+z)=y/(x+z)=z/(x+y)所以,x²+xz=y²+yz,即(x-y)(x+y+z)=0y²+xy=z²+xz,即(y-z)(x+y+z)=0若x=y=z满足x/y+z=y/x+z=z/x+y所以(x+y)/z的值为2例如：1,1,1若x+y+z=0...