Question 79539
Let the two consecutive integers be x and (x+1). From the description you can write:
{{{x*(x+1) = x+(x+1)+71}}} Simplify and solve for x.
{{{x^2+x = 2x+72}}} Subtract 2x from both sides.
{{{x^2-x = 72}}} Subtract 72 from both sides.
{{{x^2-x-72 = 0}}} Solve this quadratic equation by factoring.
{{{(x-9)(x+8) = 0}}} Apply the zero products principle.
{{{x-9 = 0}}} or {{{x+8 = 0}}} so...
{{{x = 9}}} or {{{x = -8}}}
So, there are really two answers to this problem and both would apply since the prolem did not limit the solution to positive integers.
1st. solution: x = 9 and x+1 = 10
2nd. solution: x = -8 and x+1 = -7

Check:
1st. solution:
9*10 = 90 and
9+10+71 = 90
2nd. solution:
-8*(-7) = 56 and
(-8)+(-7)+71 = -15+71 = 56

So you see, both solutions work and both sets of numbers are integers.