What two numbers add up to 4 and multiply to 6?

To find two numbers that add up to 4 and multiply to 6, let’s use two variables, x and y. We can set up the following equations based on the problem:

• x + y = 4
• x * y = 6

From the first equation, we can express y in terms of x:

y = 4 – x

Now we can substitute this expression for y into the second equation:

x * (4 – x) = 6

This simplifies to:

4x – x² = 6

Rearranging gives us a quadratic equation:

x² – 4x + 6 = 0

Next, we apply the quadratic formula:

x = (-b ± √(b² – 4ac)) / (2a)

Here, a = 1, b = -4, and c = 6. Plugging in these values:

x = (4 ± √((-4)² – 4 * 1 * 6)) / (2 * 1)

x = (4 ± √(16 – 24)) / 2

x = (4 ± √(-8)) / 2

Since the term inside the square root is negative, this means there are no real solutions for x and y under these conditions. Therefore, there are no two real numbers that both add up to 4 and multiply to 6.