Question

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

Answer 1

x-y=5;.............1
1/y  --  1/x=1/10;........2
(we have assumed x>y in 1st equation,and so 1/x will be lesser than 1/y,and the difference of reciprocal has been given positive,so we have to take 1/y (larger no) first in the 2nd equation)
now solve equation  2 with 1,and you will get xy=50; or x=y/50;
now put this value of x in 1 and solve the equation and you will get x=10 and -5;
so if x is 10 ,y is 5;and if x is 5,y is 10;
so the numbers are 10,5;

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the First number be x.

And the second number be x + 5

According to the Question,

⇒ 1/x - 1/(x + 5) = 1/10

⇒ x + 5 - x/x(x + 5) = 1/10

⇒ 5/x² + 5x = 1/10

⇒ 50 = x² + 5x

⇒ 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, 10 (As x can't be negative)

⇒ x = 10

Hence, the numbers are 5 and 10.