how can i find the numbers
Quadratic equation
the sum of 2 whole numbers is 23. their product is 120. find the numbers
To find the two numbers, we can set up a quadratic equation using the given information.
Let's say the two numbers are x and y. We know that their sum is 23, so we can write the equation:
x + y = 23
We also know that their product is 120, so we can write another equation:
xy = 120
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution. We can rewrite the first equation as:
x = 23 - y
Substituting this into the second equation, we get:
(23 - y)y = 120
Expanding and rearranging the equation, we have:
23y - y^2 = 120
Rearranging this equation in quadratic form, we have:
y^2 - 23y + 120 = 0
Now, we can solve this quadratic equation to find the values of y. We can either factor it or use the quadratic formula.
Factoring the quadratic equation, we can rewrite it as:
(y - 8)(y - 15) = 0
Setting each factor equal to zero, we have two possible solutions for y:
y - 8 = 0 --> y = 8
y - 15 = 0 --> y = 15
Now that we have the two possible values for y, we can substitute them back into the first equation to find the corresponding values of x.
For y = 8:
x + 8 = 23
x = 23 - 8
x = 15
For y = 15:
x + 15 = 23
x = 23 - 15
x = 8
Therefore, the two numbers that satisfy the given conditions are 8 and 15.