Question

The sum of the reciprocals of two consecutive odd natural number is 12÷35.find those numbers.
Give the answer of both the question

Answer 1

Answer:

Those numbers are 5 and 7.

Step-by-step explanation:

Two consecutive odd numbers: n and n + 2.

1 / n + 1 / (n + 2) = 12/35  / * n ( n + 2 )

n + 2 + n = 12/35 n ( n + 2 )  / * 35

70 n + 70 = 12 ( n²  + 2 n )

70 n + 70 = 12 n² + 24 n

12 n²  - 46 n - 70 = 0  / : 2

6 n²  - 23 n - 35 = 0

We solve the quadratic equation.

n 1/2 = (23 +/- sqrt(529 + 840) / 12

n = (23 + 37) / 12    ( other solution is negative so it is not a natural number )

n = 5,  and n + 2 = 7.

We can prove it:  1/5 + 1/7 = (7+5) / 35 = 12 / 35.