Question 230134
Find two consecutive integers such that the sum of the reciprocal of the smaller
 number and the reciprocal of the square of the larger number is the same as the
 reciprocal of the product of the smaller number and the square of the larger number?

Two numbers, x, (x+1)
:
{{{1/x}}} + {{{1/((x+1)^2)}}} = {{{1/(x(x+1)^2)}}} 
:
(x+1)^2 + x = 1
:
x^2 + 2x + 1 + x = 1
:
x^2 + 3x + 1 - 1 = 0
:
x^2 + 3x = 0
:
x(x+3) = 0
:
x = 0
x = -3
:
The two consecutive numbers: -3, -2
:
:
Check solution in original equation
{{{1/(-3)}}} + {{{1/((-2)^2)}}} = {{{1/(-3(-2)^2)}}}
{{{-1/3)}}} + {{{1/4}}} = {{{1/(-3(4))}}}
{{{-1/3)}}} + {{{1/4}}} = {{{-1/12)}}}