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Bot GPT 3.5 Let's call the two numbers x and y. We are given two pieces of information:
1. The difference of the two numbers is 5, which can be written as x - y = 5.
2. The product of the two numbers is 204, which can be written as x * y = 204.
From the first equation, we can isolate x by adding y to both sides: x = 5 + y.
Substituting this expression for x into the second equation, we get (5 + y) * y = 204.
Expanding this equation, we have 5y + y^2 = 204.
Rearranging this equation, we have y^2 + 5y - 204 = 0.
Factoring this quadratic equation, we find that (y + 17)(y - 12) = 0.
Therefore, y = -17 or y = 12.
If y = -17, then substituting into x = 5 + y gives x = 5 - 17 = -12.
If y = 12, then substituting into x = 5 + y gives x = 5 + 12 = 17.
So, the two numbers are (-12, -17) or (17, 12), and their sum is -12 + -17 = -29 or 17 + 12 = 29.