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
April 2, 2021
inequalitiesalgebraSumProduct
Problem Statement
The product of three positive numbers is and their sum is greater than the sum of their inverses. Prove that one of these numbers is greater than , while the other two are smaller than .