Question
What 2 numbers when multiplied you get 21.25, but when added you get -11
Answers
GPT 3.5
Let's call the two numbers x and y. We are given that when multiplied, they equal 21.25, so we can write the equation:
xy = 21.25
We are also given that when added, they equal -11, so we can write the equation:
x + y = -11
To solve these two equations, we can use substitution. Solving the second equation for y, we get:
y = -11 - x
Substituting this expression for y in the first equation, we have:
x(-11 - x) = 21.25
Expanding and simplifying this equation, we get:
-11x - x^2 = 21.25
Rearranging this equation, we have:
x^2 + 11x + 21.25 = 0
We can now solve this quadratic equation for x. However, upon solving, we find that the quadratic equation does not have real roots. Therefore, there are no two real numbers that satisfy the given conditions (multiplication equals 21.25 and addition equals -11).
xy = 21.25
We are also given that when added, they equal -11, so we can write the equation:
x + y = -11
To solve these two equations, we can use substitution. Solving the second equation for y, we get:
y = -11 - x
Substituting this expression for y in the first equation, we have:
x(-11 - x) = 21.25
Expanding and simplifying this equation, we get:
-11x - x^2 = 21.25
Rearranging this equation, we have:
x^2 + 11x + 21.25 = 0
We can now solve this quadratic equation for x. However, upon solving, we find that the quadratic equation does not have real roots. Therefore, there are no two real numbers that satisfy the given conditions (multiplication equals 21.25 and addition equals -11).