Question 89062


   the product of two consecutive positive even integers is 288.  Find the integers

           Let the first even number be = x
             the second  even number is = x+2
               product of even integers = 288
                               x(x+2) = 288
                                 x^2+2x-288 = 0
                                 x^2+18x-16x-288 = 0
                                 x(x+18)-16(x+18) = 0
                                     (x+18).(x-16) = 0
                        since the numbers are positive integers  we 
                          consider only  (x-16) = 0
                                          x = 16 
                                         x+2 = 16+2 = 18

    The two numbers (even  consecutive)  are 16  and 18.