Question 963811
N=smallest integer; N+2=middle integer; N+4=largest integer
{{{(N)(N+2)=4(N+N+2+N+4)+15}}}
{{{N^2+2N=4(3N+6)+15}}}
{{{N^2+2N=12N+24+15}}} Subtract 12N from each side.
{{{N^2-10N=39}}} Subtract 39 from each side.
{{{N^2-10N-39=0}}}
{{{(N-13)(N+3)=0}}}
{{{N-13=0}}} or {{{N+3=0}}}
{{{N=13}}} or {{{N=-3}}}
ANSWER 1: The smallest integer is 13.
N+2=13+2=15 ANSWER 2: The middle integer is 15.
N+4=13+4=17 ANSWER 3: The largest integer is 17.
CHECK:
{{{(N)(N+2)=4(N+N+2+N+4)+15}}}
{{{(13)(15)=4(13+15+17)+15}}}
{{{195=4(45)+15}}}
{{{195=180+15}}}
{{{195=195}}}