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at least one of a,b,c >17/10 if a,b,c>0 with a+b+c = abc

Source: 2023 NZMO - New Zealand Maths Olympiad Round 2 p2

September 2, 2023

algebrainequalities

Problem Statement

Let

a, b

and

c

be positive real numbers such that

a+b+c = abc

. Prove that at least one of

a, b

c

is greater than

\frac{17}{10}