Question

the sum of the reciprocals of two consecutive odd number natural numbers is 12 / 35 . Find those numbers .
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.THE FIRST ONE TO ANSWER CORRECT WILL BE MARKED AS BRAINLIST

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

 

The integers are 5 and 7.

 

Answer 2

let the consecutive odd numbers be x and x+2
thus, 1/x +1/x+2 =12/35
by solving this we get x=5,7