Question

Find two numbers whose difference is 44 and whose product is a minimum _______.

a) Polynomial equations
b) Quadratic functions
c) Systems of equations
d) Optimization

Answer 1

To find two numbers whose difference is 44 and whose product is a minimum, we can use quadratic functions and find the minimum value of a quadratic function to get one of the numbers.

Step-by-step explanation:

To find two numbers whose difference is 44 and whose product is a minimum, we can use quadratic functions. Let's assume the two numbers as x and y. Since their difference is 44, we can write the equation x - y = 44. To minimize the product xy, we can square the equation: (x - y)^2 = 44^2. Expanding the equation, we get x^2 + y^2 - 2xy = 1936. Since we want to find the minimum value, we can rewrite the equation as a quadratic function: f(x) = x^2 - 2(44)x + 1936. We can now find the minimum value of the function by completing the square or using vertex form. The x-coordinate of the vertex will give us the number x that minimizes the product xy.