Problema Solution
The product of a positive even integer and the reciprocal of the next larger positive integer equals the reciprocal of the first integer. Find the integer.
Answer provided by our tutors
let
2x = the positive even integer where x is positive integer
1/2x is the reciprocial of the previous number
2x + 1 is the next larger positive integer
1/ (2x + 1) the reciprocal
2x*(1/(2x + 1)) = 1/2x multiply both sides by 2x(2x + 1)
(2x)^2 = 2x + 1
4x^2 - 2x - 1 = 0
by solving the quadratic equation we find the solutions
x1 = - 0.309
x2 = 0.809
the solutions are not non-negative integer numbers thus there is no solution for the problem.