MathDB

min A=x+1/x+y+1/y if 2(x+y)=1+xy for x,y>0 , 2020 ISL A3 for juniors

Source: 2021 Greece JMO p1 (serves also as JBMO TST) / based on 2020 IMO ISL A3

July 21, 2021

algebrainequalities

Problem Statement

If positive reals

x,y

are such that

2(x+y)=1+xy

, find the minimum value of expression

A=x+\frac{1}{x}+y+\frac{1}{y}