Question 335725
Let the first integer be x, then the next consecutive integr is x+1
{{{x*(x+1) = x+(x+1)+11}}} " The product of two consecutive numbers is 11 more than their sum." Simplify this equation.
{{{x^2+x = 2x+12}}} Subtract 2x from both sides.
{{{x^2-x = 12}}} Now subtract 12 from both sides.
{{{x^2-x-12 = 0}}} Factor this trinomial.
{{{(x+3)(x-4) = 0}}} Apply the zero product rule.
{{{x+3 = 0}}} or {{{x-4 = 0}}} therefore...
{{{x = -3}}} or {{{x = 4}}} these are the two integers.
Check:
{{{x*(x+1) = x+(x+1)+11}}} Substitute x = 4.
{{{4*(5) = 4+(5)+11}}}
{{{20 = 9+11}}}
{{{20 = 20}}}
You can check x = -3 yourself.