Question

The product of two consecutive integers is 72. Find all solutions.

Answer 1

its 8*9 and I think that is the only solution... cause it says consecutive

Answer 2

Answer with Step-by-step explanation:

Let the two consecutive integers be x and x+1

Then, x(x+1)=72

         x²+x-72=0

        x²+9x-8x-72=0

       x(x+9)-8(x+9)=0

      (x-8)(x+9)=0

either x-8=0  or  x+9=0

i.e.  x=8 or x=-9

when x=8,x+1=9  and 8×9=72

when x=-9,x+1=-8 and -9×(-8)=72

Hence, two consecutive integers such that their product is equal to 72 are:

8 and 9      or      -9 and -8