Among all pairs of numbers whose difference is 16, find the pair whose product is minimum. What is the minimum product

The pair whose product is minimum is; -8 and 8.

The two numbers whose difference is 16 can be represented as;

The product of the numbers can be represented as Product, P as follows;

By completing the square technique;

In other words;

The minimum value of (x + 8)² should be equal to 0.

(x+8)² = 0

Hence, the minimum of this is when x = -8.

The pair of numbers is then;

Ultimately, the minimum product is: -8 × 8 = -64.

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-8 and 8.

Product is -64.

Step-by-step explanation:

Let the numbers be x and x + 16.

We need to find the minimum of x(x + 16).

Product P = x^2 + 16x.

Convert to vertex form:

P = (x + 8)^2 - 64

The minimum value of (x + 8)^2 = 0 so:

The minimum of this is when x = -8 ,giving P  = -64.

The pair of numbers is  -8 and -8+16 = 8

and the minimum product = -46.

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify

i think the correct option is the second option.