已知x/(y+z+t)=y/(x+z+t)=z/(x+y+t)=t/(x+y+z) 求a=(x+y)/(z+t)+(y+z)/(z+t)+(x+z)/(y+t)+(x+t)/(y+z)整

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已知x/(y+z+t)=y/(x+z+t)=z/(x+y+t)=t/(x+y+z) 求a=(x+y)/(z+t)+(y+z)/(z+t)+(x+z)/(y+t)+(x+t)/(y+z)整
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已知x/(y+z+t)=y/(x+z+t)=z/(x+y+t)=t/(x+y+z) 求a=(x+y)/(z+t)+(y+z)/(z+t)+(x+z)/(y+t)+(x+t)/(y+z)整
已知x/(y+z+t)=y/(x+z+t)=z/(x+y+t)=t/(x+y+z) 求a=(x+y)/(z+t)+(y+z)/(z+t)+(x+z)/(y+t)+(x+t)/(y+z)整

已知x/(y+z+t)=y/(x+z+t)=z/(x+y+t)=t/(x+y+z) 求a=(x+y)/(z+t)+(y+z)/(z+t)+(x+z)/(y+t)+(x+t)/(y+z)整
x/(y+z+t)=y/(x+z+t)=z/(x+y+t)=t/(x+y+z) =k
x=k(y+z+t)
y=k(x+z+t)
z=k(x+y+t)
t=k(x+y+z)
x+y+z+t=3k(x+y+z+t) 得k=1/3 得 x=y=z=t
故所求值为4

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