Question

What are the two numbers whose difference is 86, and the product is a minimum?

A) 43 and 129
B) 43 and -43
C) 86 and 0
D) -43 and -129

Answer 1

The correct answer is option B. To find the two numbers whose difference is 86 and whose product is a minimum, set up an equation and find the vertex of the resulting quadratic equation.

Step-by-step explanation:

To find the two numbers whose difference is 86 and whose product is a minimum, we can set up an equation.

Let the two numbers be x and y. We can set up the equation x - y = 86.

To minimize the product xy, we can rewrite this equation as x = y + 86.

Substituting this into the equation for the product, we get (y + 86)y.

Now, we can find the minimum value by finding the vertex of this quadratic equation.

The vertex of a quadratic equation in the form ax^2 + bx + c is given by x = -b/2a. In this case, a = 1, b = 86, and c = 0.

Plugging in these values, we find the x-coordinate of the vertex, which is -86/2(1) = -43.

Substituting this value back into the equation x = y + 86, we find that y = -43 + 86 = 43.

Therefore, the two numbers whose difference is 86 and whose product is a minimum are 43 and -43.