Question

若 x/(y+z+t)=y/(z+t+x)=z/(t+x+y)=t/(x+y+z) ,f=(x+y)/(z+t)+(y+

Answer 1

若x+y+z+t不等于0,由等比性质得：

x/(y+z+t)=y/(z+t+x)=z/(t+x+y)=t/(x+y+z)=1/3

所以：

y+z+t=3x

z+t+x=3y

t+x+y=3z

x+y+z=3t

解得：x=y=z=t

所以f=a,为整数

若x+y+z+t=0,则f=-1+(-1)+(-1)+(-1)=-4,也是整数