Question

the difference of two numbers is 5 and the difference of their reciprocal is1/10 find the number

Answer 1

Let the two numbers b x and y

According to the question
x - y = 5
x = 5 + y

The difference of the reciprocal is 1 by 10

So 1/x - 1/y = 1/10

1/ 5+y - 1/ y = 1/10

By taking the LCM we will get

5 + y - y / y2 + 5y = 1/10

by cross multiplication we will get

50 = y2 + 5y

y2 + 5y - 50 = 0

y2 + 10y - 5y - 50 = 0

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

( y + 10 ) ( y - 5 )

y = - 10 ( negative value is not possible)

y = 5