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

Respuesta :

oscar236

Answer:

-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.

adioabiola

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

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

  • x and (x+16)

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

  • P = x(x +16)

  • P = x² +16x

By completing the square technique;

  • P = (x + 8)² -64.

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;

  • x = -8 and

  • (x+16) = -8 +16 = 8

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

Read more;

https://brainly.com/question/9418842

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