Question 370862
The difference of the reciprocals of two consecutive integers is 1/72.
 Find the integers.
:
Two integers, x, (x+1)
:
{{{1/x}}} - {{{1/((x+1))}}} = {{{1/72}}}
Multiply by 72x(x+1)
results:
72(x+1) - 72x = x(x+1)
:
72x + 72 - 72x = x^2 + x
72x's cancel, a quadratic equation
x^2 + x - 72 = 0
Factor this to
(x+9)(x-8) = 0
Two solutions
x = -9, -8
and
x = +8, 9