4

Part of 1995 Swedish Mathematical Competition

Problems(1)

0<a,b<1<c if a,b,c>0 with abc=1, a+b+c>1/a+1/b+1/c

Source: 1995 Swedish Mathematical Competition p4

The product of three positive numbers is

1

and their sum is greater than the sum of their inverses. Prove that one of these numbers is greater than

1

, while the other two are smaller than

1

inequalitiesalgebraSumProduct