Question

9
The sum of two natural numbers is 9 and the sum of their reciprocals is9/20
Find the numbers.
20​

Answer 1

Answer:

5 &4

Step-by-step explanation:

Let the first natural number be x.

The second natural number = y

A/Q,

x+y = 9

x = 9 -y

Again,

Reciprocal of x + Reciprocal of y = 9/20

=> 1/x + 1/y = 9/20

=> (y+x)/xy = 9/20

=> 20(y+x) = 9 × xy

=> 20(y+9-y) = 9y(9-y)

=> 20×9 = 81y - 9y²

=> 9y²-81y+180 =0

=> 9y² -45y -36y+180 =0

=> 9y(y - 5) - 36(y - 5) =0

=> (y - 5)(9y-36) =0

y = 5

x = 9-y = 9 - 5 = 4

Therefore, two natural numbers are 5 and 4.