Question 125400
{{{n}}} is the 1st number
{{{n + 2}}} is the 2nd number
{{{(1 / n) + (1 / (n + 2)) = 7/24}}}
multiply both sides by {{{n*(n+2)}}}
{{{(n + 2) + n = (7/24)*n*(n + 2)}}}
multiply both sides by 24
{{{24*(2n + 2) = 7n^2 + 14n}}}
{{{48n + 48 = 7n^2 + 14n}}}
{{{7n^2 - 34n - 48 = 0}}}
{{{(7n + 8)(n - 6) = 0}}}
{{{n = -(8/7)}}}
I reject this since it's not a whole number and negative
and
{{{n = 6}}}
{{{n + 2 = 8}}}
The numbers are 6 and 8
check:
{{{(1/6) + (1/8) = 7/24}}}
multiply both sides by 48
{{{8 + 6 = 14}}}
{{{14 = 14}}}
OK