已知A>B>C,则1/(A-B)+1/(B-C)+1/(C-A)的正负

Question

已知A>B>C,则1/(A-B)+1/(B-C)+1/(C-A)的正负

Answer 1

设A-B=X,B-C=Y,(X,Y>0);则:C-A=-(X+Y);原式=1/X+1/Y-1/(X+Y)=(X^2+Y^2+XY)/[XY(X+Y)]>0,得数为正.