Question 134130
The odd integers are spaced every 2 numbers
{{{1,3,5,7,9}}}. . .etc.
Call the smallest odd integer {{{n}}}
The next odd integer will be {{{n + 2}}}
The product of these integers is {{{n*(n + 2)}}}
Three times their sum is {{{3*(n + (n +2))}}}
{{{n*(n+2) = 3*(n + (n + 2)) - 1}}}
{{{n^2 + 2n = 3*(2n + 2) - 1}}}
{{{n^2 + 2n = 6n + 6 - 1}}}
{{{n^2 - 4n - 5 = 0}}}
{{{(n - 5)(n + 1) = 0}}}
{{{n = 5}}}
{{{n = -1}}} This choice is not what is wanted
If {{{n = 5}}}, then
{{{n + 2 = 7}}}
The integers are 5 and 7
check answer
{{{n*(n+2) = 3*(n + (n + 2)) - 1}}}
{{{5*(5+2) = 3*(5 + (5 + 2)) - 1}}}
{{{35 = 3*(12) - 1}}}
{{{35 = 36 - 1}}}
{{{35 = 35}}}
OK