Yay for Calculus! First, use the equation: xy=S This is x times y is equal to sum, or S. Then, use the equation x + y = 200. Then, solve for x or y. I will solve for y. Doing so gives me the equation y = 200 - x Next, use this value for y in the equation xy = S. Give: x(200-x) = S Simplify: 200x - x^2 = S. Take the derivative: 200 - 2x = S' Set it equal to 0 for critical numbers: 200 - 2x = 0 Solve: -2x = -200 Solve: 2x = 200 Sove: x = 100, which is one of your integers. The other is also 100.
