Question

the sum of reciprocal of two consecutive odd natural number is 12/35 find those numbers

Answer 1

Let the two consecutive odd natural numbers are x and x+2.

As given sum of reciprocal of two consecutive odd natural number is 12/35 .

Writing the statement in terms of equation:

→1 /x   + 1/(x+2) = 12/35

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

→35× (2 x +2) = 12× (x² +2 x)

→ 70 x + 70 = 12 x² + 24 x → [ Using Distributive property: a× (b+c)  = a ×b + a× c]

Taking variable and constant on one side of equation

→ 12 x² + 24 x - 70 x - 70 =0

→ 12 x² - 46 x - 70=0

→ 2 × (6 x² - 23 x -35) =0

→ 6 x² - 23 x -35=0

Splitting the middle term

→ 6 x² - 30 x + 7 x - 35=0

→ 6 x × ( x -5) + 7 × (x -5) =0

→ (6 x +7)(x-5) =0

→ 6 x +7 =0 ∧ x -5 =0

x ≠ $\frac{-7}{6}$ can't be the solution as x is a natural number.  and x = 5.

So, x = 5  and 5+2 =7 are those two numbers whose sum is $\frac{12}{35}$.

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.