Question

X>Y>Z,试确定1/(X-Y)+1/(Y-Z)+1/(Z-X)的符号

Answer 1

X>Y>Z => X-Z>Y-Z>0 =>00

1/(X-Y)+1/(Y-Z)+1/(Z-X)=1/(X-Y)+1/(Y-Z)-1/(X-Z)

=1/(X-Y)+(1/(Y-Z)-1/(X-Z))

>1/(X-Y)+0 >0

1/(X-Y)+1/(Y-Z)+1/(Z-X)的符号为正