Question

If difference of two number is 5 and difference of of their reciprocal is 5/14. Find the two number.

Answer 1

x-y=5
1/x-1/y=5/14

x=5+y
Substitute in place of 1/x
Take lcm of denominator
Simpify

Answer 2

Hi !

Let the no:s be x and y

x - y = 5
x = y + 5

1/x - 1/y = 5/14

1/y+5 - 1/y = 5/14

y- [ y+5 ] / y² + 5y = 5/14

5/y² + 5y = 5/14

5 ( y² + 5y ) = 14 x 5
5y² + 25y = 70

5y² + 25y - 70 = 0

dividing by 5 ,

y² + 5y - 14 = 0

splitting the middle term ,
(y + 7 ) ( y - 2) = 0

y = -7 , y = 2

=======================
x - y = 5

x - 2 = 5

x = 5 + 2 = 7

=========================

The no:s are 7 and 2