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Q.

The difference between two natural numbers is Question Image and the difference of their reciprocals is Question Image. Find the numbers.


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a

 Question Image

b

 Question Image

c

 Question Image

d

 Question Image

answer is B.

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Detailed Solution

Concept-  Assume two natural numbers be variables i.e., Question Image. Now use the given condition i.e., difference of Question Image is Question Image (Question Image) and second equation will be difference of the reciprocals of variables is Question Image (Here, reciprocal is positive. Therefore, Question Image) . Solve both the required linear equations of two variables.
Let, two natural numbers be Question Image and Question ImageGiven that,
The difference between two natural numbers is Question ImageQuestion ImageOr Question ImageAnd the difference of their reciprocals is Question Image  which is positive. Therefore, Question ImageQuestion ImageQuestion ImageQuestion ImageQuestion ImageNow, using algebraic identity
Question ImageQuestion ImageQuestion ImageQuestion ImageAdding equation (1) and (2) ,
We get Question ImageQuestion ImagePut Question Image in equation (2)
It implies that Question ImageHence, the correct answer is option (2) .
 
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