Which two numbers multiply to give you 100 and add to give you 10?

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 :)

Answered by and1morefun | 2024-06-10

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 = 2 a − b ± b 2 − 4 a c ​ ​ = 2 ( − 1 ) − 10 ± 1 0 2 − 4 ( − 1 ) ( − 100 ) ​ ​ = − 2 − 10 ± 100 − 400 ​ ​ = − 2 − 10 ± − 300 ​ ​
There is no real square root of -300, so there are no real number solutions to this.

Answered by MsEHolt | 2024-06-25

There are no real numbers that multiply to give 100 and add to give 10. The equations lead to a situation where the square root of a negative number is involved, indicating no real solutions exist. Thus, the problem has no solution in the real number system.
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Answered by MsEHolt | 2024-09-03