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minimum of 1/a + 1/b + 1/c

Source: Vietnam TST 2001 for the 42th IMO, problem 4

June 26, 2005
inequalitiesinequalities unsolvedalgebrainequalities proposed

Problem Statement

Let’s consider the real numbers a,b,ca, b, c satisfying the condition 21⋅a⋅b+2⋅b⋅c+8⋅c⋅a≤12.21 \cdot a \cdot b + 2 \cdot b \cdot c + 8 \cdot c \cdot a \leq 12. Find the minimal value of the expression P(a,b,c)=1a+1b+1c.P(a, b, c) = \frac{1}{a} + \frac{1}{b} + \frac{1}{c}.
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