Question 191912
The difference between the reciprocal of two consecutive positive even number is 1/12. Find the two numbers.:
:
Two numbers x, (x+2)

:
The equation for the above statement:
{{{1/(x+2)}}} - {{{1/x}}} = {{{1/12}}}
;
Multiply equation by 12x(x+2)
12x(x+2)*{{{1/(x+2)}}} - 12x(x+2)*{{{1/x}}} = 12x(x+2)*{{{1/12}}}
Cancel out the denominators and you have:
12x - 12(x+2) = x(x+2)
:
12x - 12x + 24 = x^2 + 2x
:
0 = x^2 + 2x - 24; a quadratic equation
Factors to:
(x+6)(x-4) = 0
positive solution
x = 4, and 6 are the two numbers
;
:
Check solution in our original equation
{{{1/4}}} - {{{1/6}}} = {{{1/12}}}
{{{3/12}}} - {{{2/12}}} = {{{1/12}}}