To find two numbers that multiply to 2 and add to 3, let's denote the two numbers as \( x \) and \( y \).
We want:
- \( xy = 2 \)
- \( x + y = 3 \)
From the second equation, we can express \( y \) in terms of \( x \): \[ y = 3 - x \]
Now we substitute this expression for \( y \) into the first equation: \[ x(3 - x) = 2 \]
Expanding this gives: \[ 3x - x^2 = 2 \]
Rearranging the equation results in: \[ x^2 - 3x + 2 = 0 \]
Factoring the quadratic: \[ (x - 1)(x - 2) = 0 \]
Thus, the solutions are: \[ x = 1 \quad \text{or} \quad x = 2 \]
If \( x = 1 \), then: \[ y = 3 - 1 = 2 \]
If \( x = 2 \), then: \[ y = 3 - 2 = 1 \]
In conclusion, the two numbers are 1 and 2.
They multiply to give 2 and add to give 3:
- \( 1 \times 2 = 2 \)
- \( 1 + 2 = 3 \)
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