Question

which two numbers multiply to give you 100 and add to give you 10

Answer 1

which two numbers multiply to give you 100 and add to give you 10:
x*y = 100
x+y = 10

x = 10 - y
x(10-x) = 100
10x - x^2 = 100

... I don t remember the delta statment :)

Answer 2

The correct answer is:

There are no real numbers that fit these criteria.

Step-by-step explanation:

Let x and y represent the two numbers we are looking for.

x*y = 100
x+y = 10

Solving for y,
x+y-x = 10-x
y = 10-x

Substituting this into our first equation, we have:
x(10-x) = 100

Using the distributive property,
x*10 - x*x = 100
10x - x² = 100

Writing this in standard form, we need to subtract 100 from each side:
10x - x² - 100 = 100 - 100
10x - x² - 100 = 0

In standard form, this is
-x²+10x-100 = 0.

This is in the form ax²+bx+c; in our equation, a = -1, b = 10 and c = -100.

We will use the quadratic formula for this:


`x=(-b \pm √(b^2-4ac))/(2a) \\ \\=(-10\pm √(10^2-4(-1)(-100)))/(2(-1)) \\ \\=(-10\pm √(100-400))/(-2) \\ \\=(-10\pm √(-300))/(-2)`

There is no real square root of -300, so there are no real number solutions to this.