Question

The difference between two natural numbers is 5. The difference between their reciprocals is 1/10

Let the smaller number be s.

Write an equation in s

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Answer 1

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Step-by-step explanation:

Let the two numbers be x and x - 5 . 

According to the question.





⇒ x(x-5) = 50

⇒ x2 - 5x - 50 = 0 

⇒  x2 - 10x + 5x - 50 = 0 

⇒ x (x - 10) + 5 (x - 10) = 0

⇒  (x+5) (x-10) = 0

⇒   (x+5) (x-10) = 0 

⇒ x =  -5 or 10  

⇒ x = 10 (x = -5 , rejected) 

∴ Two numbers are 10 and (10-5) = 5. 

Answer 2

Answer:

let the numbers be x and y

then,

x-y=5. ............(1)

1/x-1/y= 1/10.............(2)

from (1) we get

x= 5+y

putting the value

50-y²/y=5

50-y² = 5y

y²+5y-50=0

y²+10y-5y-50 =0

y(y+10)-5(y+10) =0

(y+10)(y-5) =0

so y = 5

putting the value of y in (1)

x-5=5

x=10

Step-by-step explanation:

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