The difference to two natural number is 5 and the difference of their reciprocal is 5/14.find the number.

Asked by singh.dh | 5th Jun, 2019, 09:06: PM

Expert Answer:

Let the two natural numbers be x and y.
According to the question,
y - x = 5 .....(i)
1/x - 1/y = 5/14....(ii)
(y - x)/xy = 5/14
5/xy = 5/14
xy = 14 .....(iii)
y - x = 5
(y - x)2 = 25
y2 + x2 - 2xy = 25
x2 + y2 = 25 + 28 = 53.....(iv)
(x + y)2 = x2 + y2 + 2xy 
(x + y)2 = 53 + 28 = 81
x + y = 9.....(v)
Solving (i) and (v) we get x = 2 and y = 7

Answered by Sneha shidid | 6th Jun, 2019, 10:05: AM