The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?
$ \dfrac{12}{35} $
$ \dfrac{1}{35} $
$ \dfrac{35}{8} $
$ \dfrac{7}{32} $
Explanation:
Let the numbers be $ a $ and $ b $. Then, $ a $ + $ b $ = 12 and ab = 35.
$\therefore \dfrac{a + b}{ab} $=$ \dfrac{12}{35} $ $\Rightarrow$ $ \left(\dfrac{1}{b} +\dfrac{1}{a} \right) $=$ \dfrac{12}{35} $
$\therefore$ Sum of reciprocals of given numbers =$ \dfrac{12}{35} $