Question

Sum of two natural numbers is 8 and the difference of their reciprocal is 2/15

Find the numbers.


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Answer 1

Answer:

The numbers are 5 and 3

Step-by-step explanation:

Let the numbers be a and b

We are given that:

a + b = 8 .......(i)

and

1/b - 1/a = 2/15

=> a - b = (2/15)*ab .........(ii)

Adding (I) and (ii), we get:

2a = 8 + 2ab/15

30a = 120 + 2ab

Substituting for "b" using (i), we get: b = 8 - a

Therefore,

30a = 120 + 2a(8 - a)

30a = 120 + 16a - 2a²

30a - 16a + 2a² = 120

2a² + 14a - 120 = 0

a² + 7a - 60 = 0 ..........dividing by 2 throughout

(a + 12)(a - 5) = 0

a = -12 or a = 5

As "a" is a natural number, a = -12 is inadmissible

=> a = 5

Using (i), we get b = 8 - a

b = 8 - 5

=> b = 3

The required numbers are 5 and 3

Verification:

Sum of given numbers = 5 + 3 = 8

Difference of reciprocals = 1/3 - 1/5 = 2/15

Answer 2

Answer:

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