MathDB

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Part of 2021 Greece Junior Math Olympiad

Problems(1)

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

7/21/2021
If positive reals x,yx,y are such that 2(x+y)=1+xy2(x+y)=1+xy, find the minimum value of expression A=x+1x+y+1yA=x+\frac{1}{x}+y+\frac{1}{y}
algebrainequalities