Question

The sum of two natural numbers is 8.and the sum of their reciprocals is 8/15 find the numbers

Answer 1

let one of the real no. be x

other shall be 8-x

1/(x) + 1/(8-x) = 8/15

thus 8-x+x *15 = 8* x(8-x)

8*15 =8*(8x - x^2)

120 = 64x - 8x^2

15 = 8x - x^2

x^2 - 8x +15 = 0

thus x = 5

or

x = 3

thus the two real numbers are 3&5