Question 51433
Let x and y represent the two integers.  We now have equations {{{x+y=96}}} and {{{xy=1728}}}.  Using the second equation, let's solve for y by dividing both sides by x:  {{{(xy)/x=1728/x}}}, which simplifies to {{{y=1728/x}}}.  Now use this value of y and substitute it into the first equation thusly:  {{{x+1728/x=96}}}.  Multiplying both sides by x produces {{{x^2+1728=96x}}}.  Now subtract 96x from both sides to yield {{{x^2-96x+1728=0}}}.  Now we just have to factor this equation into (x - something) and (x - something_else), where the 'something' and 'something_else' when multiplied together produces 1728, and when added together they produce -96.<br>
The best way to do this is not by trial and error, but by using the discriminant.  *[invoke quadratic "x", 1, -96, 1728]