Question

25) The sum of two natural numbers is 9 and the sum of their reciprocal is 9/20. Find the numbers​

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.

Explaination:

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Answer 2

Answer:

4 and 5.

Step-by-step explanation:

x + y = 9

y = 9 - x

1/x + 1/y = 9/20

Removing the fractions from the above:

20y + 20x = 9xy

Substitute y = 9 - x  in the above:

20(9 - x) + 20x = 9x(9 - x)

180 - 20x + 20x = 81x - 9x^2

9x^2 - 81x + 180 = 0

x^2 - 9x + 20 = 0

(x - 5)(x - 4) = 0

x = 4, 5.

Let x = 4 then y = 9 - 4 = 5.