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