Question

帮忙解一道题！！！

若 X/(Y+Z+T)=Y/(Z+T+T)=Z/(T+X+Y)=T/(X+Y+Z),f(X)=(X+Y)/(Z+T)+(Y+Z)/(T+X)+(Z+T)/(X+Y)+(T+X)/(Y+Z).求f(X)的值

Answer 1

等比关系 分2种情况：（分子分母分别相加或相减）
1.X/(Y+Z+T)=Y/(Z+T+X)=Z/(T+X+Y)=T/(X+Y+Z)=(X+Y+Z+T)/[(Y+Z+T)+(Z+T+X)+(T+X+Y)+(X+Y+Z)]=1/3 这样得出的结果是X=Y=Z=T
所以f(X)=4
2.X/(Y+Z+T)=Y/(Z+T+X)=(X-Y)/[(Y+Z+T)-(Z+T+X)]=-1 （X,Y,Z,T不相等）
这样得出的是X+Y+Z+T=0
所以f(X)=-4

Answer 2

设：x/(y+z+t)=y/(z+t+x)=z/(t+x+y)=t/(x+y+z)=1/3
得：
y+z+t=3x
z+t+x=3y
t+x+y=3z
x+y+z=3t
所以：x=y=z=t
带入：则f=-1+(-1)+(-1)+(-1)=-4
(y/(z+t+x) ，你打错了)

Answer 3

若 X/(Y+Z+T)=Y/(Z+T+T)=Z/(T+X+Y)=T/(X+Y+Z),f(X)=(X+Y)/(Z+T)+(Y+Z)/(T+X)+(Z+T)/(X+Y)+(T+X)/(Y+Z).求f(X)的值

若 X/(Y+Z+T)=Y/(Z+X+T)=Z/(T+X+Y)=T/(X+Y+Z),f(X)=(X+Y)/(Z+T)+(Y+Z)/(T+X)+(Z+T)/(X+Y)+(T+X)/(Y+Z).求f(X)的值
题目不对吧

Answer 4

4