Question

the sum of the reciprocals of two consecutive odd natural numbers is 12 upon 35 find those number

Answer 1

Let n and n+2 be the integers.

 

Then,  1/n + 1/(n+2) = 12/35

 

Multiply by the LCD, 35n(n+2) to get:  35(n+2) + 35n = 12n(n+2)

 

                                                      70n + 70 = 12n2 + 24n

 

                                         12n2 - 46n - 70 = 0

 

                                           6n2 - 23n - 35 = 0

 

                                           (6n + 7)(n - 5) = 0

 

                                              n = -7/6 or 5

 

-7/6 is not an integer, so n = 5