Question

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Solve the Question!!!!!!

The difference between two natural numbers is 5 and their reciprocal is
$\frac{1}{10}$
Find the numbers.​

Answer 1

Answer:

(x,y)= (10,5) or (5,0)

Step-by-step explanation:

let two numbers be x and y

x-y=5

1/y-1/x=1/10

multiply everything for equation 2 with xy so

x-y=xy/10

x-y is 5 so

xy/10=5

xy=50

y=50/x subbing this value of y to first equation

x-50/x=5

x^2-5x-50=0

(x-10)(x+5)

x is 10 or 5 while y is 5 or 0 respectively

(x,y)= (10,5) or (5,0)

Answer 2

Answer:

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Your answer is :-

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. 

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