The sum of the reciprocals of 2 consecutive odd integers is 12/ 35 . Find the numbers.

Question

Its an application problem have to find 2 numbers -The sum of the reciprocals of 2 consecutive odd integers is 12/ 35 . Find the numbers.

Answer 1

1/x + 1/(x+2) = 12/35

35(x+2) + 35x = 12x(x+2)

35x + 70 + 35x = 12x^2 +24x

12x^2 -46x - 70 = 0

6x^2 -23x -35 = 0

it should factor

but if you don't see it

try the quadratic formula

x = 23/12 +/-(1/12)sqr(23^2 +24(35))

= (23 +/-37)/12 = -14/12 or 60/12 = 5

the two consecutive odd integers are 5 and 7

1/5 +1/7 = 12/35

7/35 +5/35 = 12/35