We're gonna solve this using optimization
First set up two equations:
xy = 784
S = x+y (our sum equation)
We are going to solve for y in the first equation to get y=784/x
Now we plug this value into the second equation to get S = x+(784/x)
Now take the derivative of this equation which will give us dS/dx = 1-(784/x^2)
When we solve for x we get x = 28 and x=-28. If you notice, the derivative goes from negative to positive at 28 so this is where the minimum of the sum occurs.
Now we plug in x = 28 into the first equation and solve 28y=784 to get y=28
Now it's simple we just plug these two numbers into our sum equation to get a minimum sum of 28+28 =56
Hope this helped :)
