JAMB - Mathematics (1989 - No. 23)
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
r > \(\frac{abc}{bc + ac + ab}\)
r < abc
r > \(\frac{1}{a}\) + \(\frac{1}{b}\) + \(\frac{1}{c}\)
. \(\frac{1}{abc}\)
Vysvětlení
\(\frac{r}{a}\) + \(\frac{r}{b}\) + \(\frac{r}{c}\) > 1 = \(\frac{bcr + acr + abr}{abc}\) > 1
r(bc + ac + ba > abc) = r > \(\frac{abc}{bc + ac + ab}\)
r(bc + ac + ba > abc) = r > \(\frac{abc}{bc + ac + ab}\)