Answer:
{2, 52}
Step-by-step explanation:
Actually, there are two answers, not just one.
Let the numbers be x and y.
Then their sum is x + y and equals 52.
Their product is xy and equals 100.
We need to solve this system of equations for both x and y.
Solving x + y = 52 for x, we get x = 52 - y.
Substituting this result into the other equation, we get:
(52 - y)y = 100
This is a quadratic equation: 52y - y² = 100, or
-y² + 52y - 100 = 0.
Alternatively, y² - 52y + 100 = 0
Let's solve this quadratic by "completing the square."
First, identify the coefficient of the y term. It is -52. Take half of that, obtaining -26, square this result, obtaining 676. Add 676 to y² - 52y, and then subtract 676 from the result:
y² - 52y + 676 - 676 + 100 = 0.
Then (y -26)² = 576.
Taking the square root of both sides, we get:
y - 26 = ± 24, or:
y = 24 + 26 = 50, and also:
y = -24 + 26 = 2
Note that 2(50) = 100, as it must, and that
2 + 50 = 52 (also correct).
The two-part answer is {2, 52}.
The numbers are 2, and 50 if the sum of two numbers is 52. Their product is 100.
Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
Let x be the number the second number will be (52-x)
Their product is 100
x(52-x) = 100
52x - x² = 100
- x² + 52x - 100 = 0
After solving the quadratic equation:
x = 2, x = 50
Thus, the numbers are 2, and 50 if the sum of two numbers is 52. Their product is 100.
Learn more about quadratic equations here:
brainly.com/question/2263981
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