Question

The sum of two natural number is 9 and the sum of their reciprocal is
find the numbers.
$\frac{9}{20}$
​

Answer 1

Answer:

• The two numbers are 5 and 4

Step-by-step explanation:

• Let the numbers be x and y

Given:

• (i) Sum of the two natural numbers is 9

• x + y = 9 …(1)

• (ii) Sum of their reciprocals is 9/20

• 1/x + 1/y = 9/20

• (x + y)/xy = 9/20 … (2)

• Using (1) in (2)

• 9/xy = 9/20

 

• xy = 20 …(3)

• Using (1) in (3)

• x(9 - x) = 20

• x^2  -9x + 20 = 0

• (x - 5)(x - 4) = 0  

• x = 5 or x = 4 …(4)

• Using (4) and (1),  

• If x = 5, then y = 4.

• If x = 4, then y = 5.

The two natural numbers are 4 and 5.