The sum is 1.7 and the product is 6.3. What are the numbers?
To find the two numbers that have a sum of 1.7 and a product of 6.3, we can set up a system of equations and solve it.
Let's denote the two numbers as x and y.
From the given information, we have two equations:
Equation 1: x + y = 1.7
Equation 2: x * y = 6.3
We can solve this system of equations by substitution or elimination method. Here, we'll use the substitution method.
From Equation 1, we can solve for one variable in terms of the other. Let's solve for x:
x = 1.7 - y
Now we substitute this value of x into Equation 2:
(1.7 - y) * y = 6.3
Expanding and rearranging the equation:
1.7y - y^2 = 6.3
-y^2 + 1.7y - 6.3 = 0
This is a quadratic equation in standard form. To solve it, we can use factoring, completing the square, or the quadratic formula.
Factoring doesn't easily work for this equation, so we'll use the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = -1, b = 1.7, and c = -6.3.
Plugging in these values, we get:
y = (-1.7 ± √(1.7^2 - 4(-1)(-6.3))) / (2(-1))
Simplifying further:
y = (-1.7 ± √(2.89 - 25.2)) / (-2)
y = (-1.7 ± √(-22.31)) / (-2)
Since the square root of a negative number isn't a real number, there are no real solutions to this equation. Therefore, there is no pair of numbers that have a sum of 1.7 and a product of 6.3.
In conclusion, it is not possible to find the two numbers that satisfy the given conditions.