Answer: -16
Explanation:
Let's assume the two numbers are x and y.
Then, the sum of the two numbers will be x + y.
We know that the sum of the two numbers times the numbers separately equal to 2418 and 3666. Therefore, we can write the following two equations:
Eq 1. x(x + y) = x² + xy = 2418
Eq 2. y(x + y) = xy + y² = 3666
Now, we subtract equation 2 from equation 1:
x² + xy - (xy + y²) = 2418 - 3666
and we will get:
Eq 3. x² - y² = -1248
According to the theory x² - y² = (x + y)(x - y)
we can write our equation 3 as:
Eq 3. (x + y)(x - y) = -1248
The question asks us to find the difference between the two numbers,
which is just the (x - y) in our equation 3. It means that we need to find out the value of (x + y) now.
In order to find (x + y), we simply add equation 1 and equation 2 up:
x² + xy + (xy + y²) = 2418 + 3666
x² + 2xy + y² = 6084
and according to the theory (x + y)² = x² + 2xy + y²
we will get: (x + y)² = 6084
so (x + y) = √6084 = 78
Let's substitute the value into Eq 3. (x + y)(x - y) = -1248
we can find out that (x - y) = (-1248) ÷ (78) = -16
Therefore, we can conclude that the difference between the numbers is -16