Question

a,b,c,d均属于正实数,求证1<d/(a+b+c)+a/(b+c+d)+b/(a+c+d)+c/(a+b+d)<2 求解.....................谢谢!

Answer 1

(1)d/(a+b+c)+a/(b+c+d)+b/(a+c+d)+c/(a+b+d)>d/(a+b+c+d)+a/(b+c+d+a)+b/(a+c+d+b)+c/(a+b+d+c)=1;
(2)d/(a+b+c)+a/(b+c+d)+b/(a+c+d)+c/(a+b+d)<(d+d)/(a+b+c+d)+(a+a)/(a+b+c+d)+(b+b)/(a+b+c+d)+(c+c)/(a+b+c+d)=2.
证毕。
给些奖励呗。