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(x+1/x)(y+1/y)>=9 if x,y>0, x+y=1 OLCOMA Costa Rica Final 2016 Shortlist A3 D1

Source:

September 23, 2021

algebrainequalities

Problem Statement

Let

x

and

y

be two positive real numbers, such that

x + y = 1

. Prove that

\left(1 +\frac{1}{x}\right)\left(1 +\frac{1}{y}\right) \ge 9