Write two numbers that multiply to the value on top and add to the value on bottom

Question

6

5

Answer 1

To find two numbers that multiply to 6 and add up to 5, we can set up the equations:

\( x \cdot y = 6 \)
\( x + y = 5 \)

We can solve this by substituting \( y \) in the first equation using the second equation. From \( x + y = 5 \), we can express \( y \) as \( y = 5 - x \).

Now we can substitute \( y \) in the multiplication equation:

\[ x(5 - x) = 6 \]

This simplifies to:

\[ 5x - x^2 = 6 \]

Rearranging gives:

\[ x^2 - 5x + 6 = 0 \]

Now we can factor this equation:

\[ (x - 2)(x - 3) = 0 \]

So, \( x = 2 \) or \( x = 3 \).

Thus, the two numbers are 2 and 3.

So, the numbers are 2 and 3.