find the range of values of values of r which satisfies the following inequality, where...

JAMB 1989

find the range of values of values of r which satisfies the following inequality, where a, b and c are positive \(\frac{r}{a}\) + \(\frac{r}{b}\) + \(\frac{r}{c}\) > 1

A. r > \(\frac{abc}{bc + ac + ab}\)
B. r < abc
C. r > \(\frac{1}{a}\) + \(\frac{1}{b}\) + \(\frac{1}{c}\)
D. . \(\frac{1}{abc}\)

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Correct Answer: Option A

Explanation

\(\frac{r}{a}\) + \(\frac{r}{b}\) + \(\frac{r}{c}\) > 1 = \(\frac{bcr + acr + abr}{abc}\) > 1

r(bc + ac + ba > abc) = r > \(\frac{abc}{bc + ac + ab}\)

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