Question

The difference of two natural numbers is 5 and the difference of their reciprocal is 1/10 find the number

Answer 1

Step-by-step explanation:

the two numbers are x=10 and y=5

Answer 2

Answer:

Let the required numbers be x and (x- 5) .

Then,

x>(x -5 )

=>1/x <1/x - 5

1/x-5>1/x .

Therefore ,

1/x- 5 -1/x= 1/10 .

=> x - ( x - 5) / (x - 5) x = 1/10 .

=> 5/ (x- 5 )x=1/10 ( by cross multiplication )

=>(x-5) x = 50

=> x^2 -5x -50= 0

=> x^2 - 10x +5x - 50 = 0

=> x ( x- 10 ) +5 ( x - 10 ) =0

=> (x- 10) (x+5) =0

=> x= p10 or x = - 5

=> x = 10 ( since -5 is not a natural number)

Hence, the required natural numbers are 10 and 5 .

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