find 2 numbers whose sum is 64 and product is 960

I set this up as a polynomial

x^2-64x+960

factor this

(x - 40)(x-24)

where you it's roots to be

40 and 24

so
40 + 24 = 64
40 * 24 = 960

To find the two numbers, let's call them x and y.

We are given two conditions:
1. The sum of the numbers is 64, so we can write the equation: x + y = 64.
2. The product of the numbers is 960, so we can write the equation: x * y = 960.

To solve this system of equations, we can try to use the substitution method.

From the first equation, we can isolate one variable by expressing x in terms of y:
x = 64 - y.

Now we substitute this expression for x in the second equation:
(64 - y) * y = 960.

Let's simplify this equation:

64y - y^2 = 960.

Rearranging, we get:

y^2 - 64y + 960 = 0.

Factoring this quadratic equation, we have:

(y - 40)(y - 24) = 0.

Setting each factor equal to zero and solving for y, we get two potential values:

1. y - 40 = 0
y = 40.

2. y - 24 = 0
y = 24.

Now we substitute each value of y back into the equation x + y = 64 to find the corresponding value of x:

1. When y = 40:
x + 40 = 64
x = 64 - 40
x = 24.

So one pair of numbers is x = 24 and y = 40.

2. When y = 24:
x + 24 = 64
x = 64 - 24
x = 40.

So the other pair of numbers is x = 40 and y = 24.

Therefore, the two numbers whose sum is 64 and product is 960 are 24 and 40.

To find two numbers whose sum is 64 and product is 960, we can set up a system of equations.

Let's call the two numbers x and y.

From the given information, we can create two equations:

Equation 1: x + y = 64 (sum is 64)
Equation 2: x * y = 960 (product is 960)

To solve this system of equations, we can use substitution or elimination method.

Let's solve it using the substitution method:
From Equation 1, we can isolate y:
y = 64 - x

Substitute this value of y in Equation 2:
x * (64 - x) = 960

Expanding this equation:
64x - x^2 = 960

Rearranging to get a quadratic equation:
x^2 - 64x + 960 = 0

We can factorize this equation:
(x - 30)(x - 34) = 0

Setting each factor to zero and solving for x, we get two possible values for x:
x - 30 = 0 => x = 30
x - 34 = 0 => x = 34

Now substitute these values of x back into Equation 1 to find the corresponding values for y:
For x = 30, y = 64 - 30 = 34
For x = 34, y = 64 - 34 = 30

Therefore, the two numbers whose sum is 64 and product is 960 are 30 and 34.