Question

the difference of two natural numbers is 5 and the difference of their reciprocal is 110.Find the numbers.​

Answer 1

Step-by-step explanation:

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Answer 2

Let x and y be two natural numbers such that x>y

then Difference of the two natural numbers =x−y=5

Difference of their reciprocals =

y

1

−

x

1

=

10

1

since

y

1

>

x

1

⇒

xy

x−y

=

10

1

⇒

xy

5

=

10

1

⇒xy=

10

1

5

=50

⇒x=

y

50

Using x−y=5⇒

y

50

−y=5

⇒50−y

2

−5y=0

⇒y

2

+5y−50=0

⇒y

2

+10y−5y−50=0

⇒y(y+10)−5(y+10)=0

⇒(y+10)(y−5)=0

⇒y=−10,5

∴y=5 since y=−10 is not a natural number.

⇒x−y=5

⇒x−5=5 or x=10

∴ the required natural numbers are x=10,y=5