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Let x and y be the two numbers. We can set up a system of equations: x + y = 20 and xy = 64. By solving the first equation for y (y = 20 - x) and substituting into the second equation, we get x(20 - x) = 64. Simplifying this quadratic equation gives us x^2 - 20x + 64 = 0. Factoring this equation gives us (x - 16)(x - 4) = 0. Therefore, the two numbers are 16 and 4.
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Well, isn't that a happy little math problem we have here! Let's think about this together. The two numbers that add up to 20 and multiply to 64 are 8 and 12. Just like painting a beautiful landscape, sometimes all it takes is a little patience and a gentle touch to find the right solution.
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