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Turkey EGMO TST 2019 P2

Source: Turkey EGMO TST 2019 P2

November 25, 2019

Turkeyminimum valueinequalitiesthree variable inequalityalgebra

Problem Statement

Let

a,b,c

be positive reals such that

abc=1

a+b+c=5

and

(ab+2a+2b-9)(bc+2b+2c-9)(ca+2c+2a-9)\geq 0

. Find the minimum value of

\frac {1}{a}+ \frac {1}{b}+ \frac{1}{c}