Question

How to find two consecutive integers for a product of 1295?

Answer 1

Let the first integer be x; then the second is x+1.

The product of x and x+1 is x(x+1), and this product must equal 1295.

Thus, x^2 + x = 1295, or x^2 + x - 1295 = 0

Solve for x by completing the square:

          x^2 + x + (1/2)^2 - (1/2)^2 - 1295 = 0

           (x-1/2)^2 - 1/4 - 1295 = 0, or (x-1/2)^2 -5181/4 = 0, 
 
                Thus, x-1/2 = sqrt(5181/4), and so 

                           x      =  1/2+sqrt(5181/4) = 25.45

This could NOT be correct, since x and x+1 are CONSECUTIVE INTEGERS.

CHECK to ensure that you have copied down this problem correctly.