Two consecutive even whole numbers are selected. The difference between the reciprocals of the two numbers is 1/60. Determine the two numbers.
Accepted Solution
A:
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 [tex] \frac{1}{x+2} - \frac{1}{x} = \frac{1}{60} [/tex] we have to mulitply the 2 denominators x and (x+2) to get a common denominator for the 2 fractions [tex] \frac{x - (x+ 2)}{x(x+ 2)} [/tex] = [tex] \frac{1}{60} [/tex] we can then remove the brackets from the numerator and denominator [tex] \frac{x-x+2}{ x^{2} +2x } = \frac{1}{60} [/tex] 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