Two numbers whose sum is 30 and product is 8800? How do I find that?
Two numbers whose sum is 30 and product is 8800.
This problem cannot be solved in the real domain. It has a solution, however, in complex numbers.
Let x and y be the numbers.
(x+y)=30 => y=30-x
xy=8800 => x(30-x)=8800 =>
x²-30x+8800=0
Solve by the quadratic formula:
x=(30±√((-30)²-35200))/2
=15±5√7³ i
To find two numbers whose sum is 30 and product is 8800, you can use algebraic equations. Let's assume the two numbers are x and y.
Based on the information given, we can set up the following equations:
Equation 1: x + y = 30 (sum is 30)
Equation 2: x * y = 8800 (product is 8800)
Now let's solve these equations step by step:
Step 1: Solve Equation 1 for one variable (e.g., y) in terms of the other variable (x).
y = 30 - x
Step 2: Substitute this value of y into Equation 2.
x * (30 - x) = 8800
Step 3: Simplify and rewrite this equation in standard form.
30x - x^2 = 8800
Step 4: Rearrange the equation to form a quadratic equation in standard form.
x^2 - 30x + 8800 = 0
Step 5: Solve this quadratic equation using factoring, completing the square, or the quadratic formula.
By factoring, we can rewrite the equation as:
(x - 20)(x - 440) = 0
Therefore, x = 20 or x = 440.
Step 6: Substitute the values of x back into Equation 1 to solve for y.
If x = 20, then y = 30 - 20 = 10
If x = 440, then y = 30 - 440 = -410
Therefore, the two numbers whose sum is 30 and product is 8800 are 20 and 10.