Question

the difference of two numbers is 5 and the difference of their reciprocals is
1/10 . find the number.​

Answer 1

Answer:

10 and 5

Step-by-step explanation:

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

Now, according to the question:-

⇒1/x-5-1/x=1/10

⇒x-(x-5)/x(x-5)=1/10

⇒5/x(x-5)=1/10

⇒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)

Therefore two numbers are 10 and (10-5)=5

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