What two numbers have a product of 3.6 and a sum of 3.8
xy = 3.6
x+y = 3.8
x + 3.6/x = 3.8
x^2 - 3.8x + 3.6 = 0
(x-2)(x-1.8) = 0
x+y = 3.8 ---> y = 3.8-x
xy=3.6
plug first into 2nd
x(3.8-x) = 3.6
3.8x - x^2 - 3.6 = 0
times -10
10x^2 - 38x + 36 = 0
5x^2 - 19x + 18 = 0
(x-2)(5x - 9) = 0
x = 2 or x = 9/5 or 1.8
if x=2 , y = 3.8-2 = 1.8
if x = 1.8, y = 3.8-1.8 = 2
(symmetric answers)
the two numbers are 2 and 1.8
check:
2+1.8 = 3.8 , check!
2(1.8) = 3.6 , check!
To find two numbers with a product of 3.6 and a sum of 3.8, we can set up a system of equations.
Let's call the numbers x and y.
The product of x and y is 3.6:
x * y = 3.6
The sum of x and y is 3.8:
x + y = 3.8
We can solve this system of equations to find the values of x and y.
One way to solve this system is by substitution. We can solve one equation for one variable and substitute it into the other equation.
From the first equation, we have:
x = 3.6 / y
Substituting this expression for x in the second equation, we get:
(3.6 / y) + y = 3.8
Now, we can solve this equation to find the value of y.
Multiplying throughout by y, we get:
3.6 + y^2 = 3.8y
Rearranging the equation:
y^2 - 3.8y + 3.6 = 0
Now, we can solve this quadratic equation for y. We can either factor it or use the quadratic formula.
Factoring the equation, we can rewrite it as:
(y - 2)(y - 1.8) = 0
So, either y - 2 = 0 or y - 1.8 = 0.
Solving for y, we find two possible values:
y = 2 or y = 1.8
Substituting these values of y back into the first equation, we can find the values of x.
If y = 2, then x = 3.6 / 2 = 1.8
If y = 1.8, then x = 3.6 / 1.8 = 2
Therefore, the two numbers that have a product of 3.6 and a sum of 3.8 are 1.8 and 2.