sum=245
product=15,006
What are the two numbers?
x + y = 245
x * y = 15006
Solve for x and y
To find the two numbers with a given sum and product, we can set up and solve a system of equations.
Let's assume the two numbers as x and y.
We are given:
sum = x + y = 245 (equation 1)
product = xy = 15,006 (equation 2)
Now, we can solve this system of equations.
From equation 1, we can express y in terms of x:
y = 245 - x
Substituting this value of y into equation 2, we get:
x(245 - x) = 15,006
Expanding the equation:
245x - x^2 = 15,006
Rearranging the equation:
x^2 - 245x + 15,006 = 0
Now, we can solve this quadratic equation. We can either factor it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In our case:
a = 1
b = -245
c = 15,006
x = (-(-245) ± √((-245)^2 - 4*1*15,006)) / (2*1)
x = (245 ± √(60,025 - 60,024)) / 2
x = (245 ± √1) / 2
This gives us two possible values for x:
x1 = (245 + 1) / 2 = 246 / 2 = 123
x2 = (245 - 1) / 2 = 244 / 2 = 122
Now we can substitute the values of x into equation 1 to find the corresponding values of y:
For x = 123, y = 245 - 123 = 122
For x = 122, y = 245 - 122 = 123
Therefore, the two numbers are either 123 and 122, or 122 and 123.
To find the two numbers given their sum and product, we can set up a system of equations. Let's denote the two numbers as x and y.
1. Since the sum of the two numbers is 245, we can write the equation:
x + y = 245
2. Also, the product of the two numbers is 15,006:
xy = 15,006
To solve this system of equations, we can use substitution or elimination.
Let's solve it using the substitution method:
1. Solve equation 1 for x:
x = 245 - y
2. Substitute this expression for x in equation 2:
(245 - y)y = 15,006
3. Simplify and solve for y:
245y - y^2 = 15,006
Rearrange the equation:
y^2 - 245y + 15,006 = 0
Now, we can factor or use the quadratic formula to solve for y. In this case, factoring would be quicker:
Factoring the quadratic equation:
(y - 134)(y - 112) = 0
Setting each factor to zero and solving for y:
y - 134 = 0 or y - 112 = 0
y = 134 or y = 112
Now that we have two possible values for y, we can substitute them back into equation 1 to find the corresponding x values:
For y = 134:
x + 134 = 245
x = 245 - 134
x = 111
For y = 112:
x + 112 = 245
x = 245 - 112
x = 133
So the two numbers are 111 and 134, or 133 and 112.