Question

The sum of the reciprocals of two consecutive odd natural numbers is 12/35. Find those numbers

Answer 1

Answer:

The numbers are 5 and 7.

Step-by-step explanation:

An odd natural number is given by 2a+1, where a is any whole number.

Now let us take the two consecutive odd natural numbers to be (2x-1) and (2x+1).

It is given that the sum of their reciprocals is 12/35.

$\frac{1}{2x-1} +\frac{1}{2x+1} =\frac{12}{35}$

$\frac{(2x+1)+(2x-1)}{(2x-1)(2x+1)}=\frac{12}{35}$

35 * (4x) = 12 * (4x²-1)

35 x = 12 x² - 3

12x² - 35x -3=0

Solving the above equation using quadratic equation formula, we have

x = 3 and x = -(1/12)

The root x=-1/12 can be eliminated as the required numbers are natural numbers.

The two nos. are (2x-1) and (2x+1). Substituting x=3 in the expressions, we have the required numbers as 5 and 7.

∴ The numbers are 5 and 7.

Answer 2

Thank you for asking this question. The options for this question are missing, here are the missing options:

A. 3  

B. 5  

C. 7  

D. 9  

E. 11

Answer:

x = 5 and y = 7

1/x + 1/y

= 1/5 + 1/7

= 12/35

So the greater of the two integers is 7 so the final answer for this question is OPTION C: 7

If there is any confusion please leave a comment below.