Question

The product of two numbers is 14 and their sum is 5.
What is the sum of the reciprocals of these numbers?​

Answer 1

Given,

$xy = 14$

----(I)

and

$x + y = 5$

----(II)

Find

$\frac{1}{x} + \frac{1}{y}$

----(III)

Dividing (II) by (I),

$\frac{x + y}{xy} = \frac{5}{14}$

$\frac{x}{xy} + \frac{y}{xy} = \frac{5}{14}$

$\frac{1}{y} + \frac{1}{x} = \frac{5}{14}$

Hence proved.

Answer 2

The sum of the reciprocals of these numbers is $\dfrac{5}{14}$.

Step-by-step explanation:

Let the first number = x and second number = y

Given,

The product of two numbers = 14 and their sum = 5

To find, he sum of the reciprocals of these numbers = ?

According to question,

xy = 14  ....(1)

and,

x + y = 5    (2)

∴ $\dfrac{1}{x} +\dfrac{1}{y}$

=$\dfrac{x+y}{xy}$

Using (1) and (2), we get

$=\dfrac{5}{14}$

Hence, the sum of the reciprocals of these numbers is $\dfrac{5}{14}$.