Let the two numbers be $x$ and $y$.

The problem states that the sum of the two numbers is equal to their product. Therefore, the equation is: $x + y = xy$

We can rearrange this equation: $xy - x - y = 0$ Adding 1 to both sides: $xy - x - y + 1 = 1$ This can be factored as: $(x - 1)(y - 1) = 1$ This equation suggests that $x - 1$ and $y - 1$ are reciprocals of each other.

Let's find the values of $x$ and $y$.

• If $x - 1 = 1$ and $y - 1 = 1$, then $x = 2$ and $y = 2$.

Thus, the two numbers are $2$ and $2$.

These two numbers satisfy the condition that their sum and product are equal: $2 + 2 = 4 \quad \text{and} \quad 2 \times 2 = 4$

Answer:

The two numbers are $2$ and $2$.

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Would you like a detailed explanation of how the equation was factored or any other clarifications?

Here are 5 related questions:

1. What happens if we allow the two numbers to be different?
2. Can this problem be extended to three numbers with the same sum and product?
3. What if the two numbers are complex numbers?
4. How does this problem change in different number systems, such as integers or rationals?
5. What if the product is a given value, can we find the sum?

Tip: Factoring techniques, like completing the square or factoring by grouping, can often simplify equations and reveal solutions.