To find two numbers that multiply to 24 and add up to 2, we can set up a little algebra. Let’s call the two numbers ‘x’ and ‘y’. We know:
- x * y = 24
- x + y = 2
We can express ‘y’ in terms of ‘x’ from the second equation:
y = 2 – x
Now, we can substitute this expression for ‘y’ into the first equation:
x * (2 – x) = 24
This simplifies to:
2x – x² = 24
Rearranging gives:
x² – 2x + 24 = 0
Next, we can use the quadratic formula to find the values of ‘x’:
x = (-b ± √(b² – 4ac)) / 2a
Here, a = 1, b = -2, and c = 24:
x = (2 ± √((-2)² – 4 * 1 * 24)) / (2 * 1)
x = (2 ± √(4 – 96)) / 2
x = (2 ± √(-92)) / 2
Since the discriminant (the part under the square root) is negative, it means there are no real numbers that satisfy both conditions simultaneously. Thus, there are no two real numbers that multiply to 24 and add to 2.