Question

Two consecutive even whole numbers are selected. The difference between the reciprocals of the two numbers is 1/60. Determine the two numbers.

Answer 1

let the 2 numbers be x and x + 2
since they are 2 consecutive even numbers, the difference between them is 2
the difference between the reciprocals is 1/60 
$\frac{1}{x+2} - \frac{1}{x} = \frac{1}{60}$
we have to mulitply the 2 denominators x and (x+2) to get a common denominator for the 2 fractions 
$\frac{x - (x+ 2)}{x(x+ 2)}$ = $\frac{1}{60}$
we can then remove the brackets from the numerator and denominator 
$\frac{x-x+2}{ x^{2} +2x } = \frac{1}{60}$
and then cross multiply
60 * 2 = x² + 2x
120 = x² + 2x
x² + 2x - 120 = 0
we have a quadratic equation which needs to be solved 
x² + 12x - 10x - 120 = 0
x (x + 12) - 10(x + 12) = 0
(x - 10) (x + 12) = 0
x - 10 = 0     or   x + 12 = 0
x = 10                x = -12
since we haven't been told if the whole numbers are positive or negative, 
2 numbers could be 10 and 12 
or
- 12 and - 10