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Write two numbers that multiply to the value on top and add to the value on bottom.
3
4
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Attempt 5 out of 5

Answer 1

To find two numbers that multiply to 3 and add to 4, let's denote the two numbers as \( x \) and \( y \). We need to satisfy the following equations:

1. \( x \times y = 3 \)
2. \( x + y = 4 \)

To solve this, we can express \( y \) in terms of \( x \) using the second equation:

\[ y = 4 - x \]

Now, we can substitute this expression for \( y \) into the first equation:

\[ x \times (4 - x) = 3 \]

Expanding this gives:

\[ 4x - x^2 = 3 \]

Rearranging the equation:

\[ -x^2 + 4x - 3 = 0 \]

We can multiply the whole equation by -1 to make it easier to solve:

\[ x^2 - 4x + 3 = 0 \]

Now, we can factor this quadratic equation:

\[ (x - 1)(x - 3) = 0 \]

Setting each factor to zero gives us:

1. \( x - 1 = 0 \) → \( x = 1 \)
2. \( x - 3 = 0 \) → \( x = 3 \)

Now we find the corresponding \( y \) values using \( y = 4 - x \):

- If \( x = 1 \), then \( y = 4 - 1 = 3 \).
- If \( x = 3 \), then \( y = 4 - 3 = 1 \).

Thus, the two numbers that multiply to 3 and add to 4 are 1 and 3.

**Answer: 1 and 3**