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问题: S=a/(a b d) b/(a b c) c/(a d c) d/(a c d) 那么S的取值范围是?

S=a/(a+b+d)+b/(a+b+c)+c/(a+d+c)+d/(a+c+d) 那么S的取值范围是?

答案 1<S<2 求详解 没记错是那个答案

解答:

a/(a+b+c+d)<a/(a+b+d)<a/(a+b),
b/(a+b+c+d)<b/(a+b+c)<b/(a+b),
c/(a+b+c+d)<c/(a+d+c)<c/(c+d),
d/(a+b+c+d)<d/(a+c+d)<d/(c+d),
以上四式相加可得:1<S<2