Question

Two consecutive even whole numbers are selected. The difference between the reciprocals of the two numbers is 1/40. determine the two numbers

Answer 1

2 numbers could be 10 and 12

or - 12 and - 10

Explanation:

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

we have to mulitply the 2 denominators x and (x+2) to get a common denominator for the 2 fractions

=

we can then remove the brackets from the numerator and denominator

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