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 -
C.
r > (frac{1}{a}) + (frac{1}{b}) + (frac{1}{c}) -
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})