Find two consecutive positive odd numbers given that the difference between thwir reciprocals is 2/63.

Question

Solving quadratic equation.

Answer 1

Let the consecutive odd numbers be x and x+2.  The difference of their reciprocals is 2/63:

 

1/x - 1/(x+2) = 2/63

 

Put the two fractions over a common denominator, x(x+2):

 

(x+2)/x(x+2) - x/x(x+2) = 2/x(x+2) = 2/63

 

Hence:

 

x(x+2) = 63

x² + 2x - 63 = 0

 

Factors to:

 

(x+9)(x-7) = 0

 x = -9 and 7

 

There are two solutions: {-9,-7} and {7,9}