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Find minimum value

Source: Bosnia and Herzegovina TST 2015 day 1 problem 1

May 16, 2015
inequalitiesminimum value

Problem Statement

Determine the minimum value of the expression a+1a(a+2)+b+1b(b+2)+c+1c(c+2)\frac {a+1}{a(a+2)}+ \frac {b+1}{b(b+2)}+\frac {c+1}{c(c+2)} for positive real numbers a,b,ca,b,c such that a+b+c≤3a+b+c \leq 3.
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