What two numbers have a product of 3.6 and a sum of 3.8?
let one number be x
the other is 3.8-x
x(3.8-x) = 3.6
3.8x - x^2 = 3.6
times -10
10x^2 - 38x + 36 = 0
5x^2 - 19x + 18 = 0
(x-2)(5x-9) = 0
x = 2 or x = 9/5 which is 1.8
so one number is 2, the other is 3.8-2 = 1.8
check (2)(1.8) = 3.6
2 + 1.8 = 3.8
what is the product o 3.6=
To find the two numbers, let's assign variables to them. Let's call the first number 'x' and the second number 'y'.
We know that the product of the two numbers is 3.6, so we can write the equation:
x * y = 3.6 (Equation 1)
We also know that the sum of the two numbers is 3.8, so we can write another equation:
x + y = 3.8 (Equation 2)
To solve these two equations simultaneously, we can use a method called substitution. Rearrange Equation 2 to solve for one variable in terms of the other. Let's solve for x:
x = 3.8 - y
Now, substitute this value of x into Equation 1:
(3.8 - y) * y = 3.6
Expand the equation and simplify:
3.8y - y^2 = 3.6
Rearrange to form a quadratic equation:
y^2 - 3.8y + 3.6 = 0
Now we have a quadratic equation. We can solve it using factoring, completing the square, or the quadratic formula. In this case, factoring might be the simplest method.
Factor the quadratic equation:
(y - 2)(y - 1.8) = 0
Set each factor equal to zero and solve for y:
y - 2 = 0 --> y = 2
y - 1.8 = 0 --> y = 1.8
It seems we have two possible values for y. Now we need to substitute these values back into Equation 2 to find the corresponding values for x:
For y = 2:
x + 2 = 3.8 --> x = 1.8
For y = 1.8:
x + 1.8 = 3.8 --> x = 2
So the two numbers that have a product of 3.6 and a sum of 3.8 are 1.8 and 2, or 2 and 1.8.