Question

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

Answer 1

Answer:

Step-by-step explanation:

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

→

→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 ≠  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 .

Answer 2

hope it will help you