Question

The sum of two numbers is 16. The sum of their squares is a minimum. Determine the number

Answer 1

WHAT DOES THIS MEAN D:

Answer 2

Let the two numbers be: x and (16-x)
You need to minimize x^2 + (16-x)^2

Answer 3

x^2 + (16-x)^2 is a vertical parabola that opens upward. Minimum will be at the vertex.

Answer 4

8,8

Answer 5

its saying the sum of 2 numbers which is x and y so the equation can be like
x + y = 16 or y = -x + 16
the sum of two squares can be written as
x^2 + y^2 because of the first equation
then x^2 + (-x + 16)^2 = x^2 + (-x +16)(-x + 16)
then expand the binomial
you will get x^2 + x^2 - 16x - 16x + 256
2x^2 - 32x + 256

Answer 6

x^2 + (16-x)^2
=2x^2 -32x +196
=2(x-8)^2 +132
so min when x=8

Answer 7

there are 2 ways to find the minimum for that function -b/2a
-32/4 = 8

Answer 8

x^2 + (16-x)^2 =2x^2 -32x +256 (error in calculation)
=2(x-8)^2 +192
so min when x=8

Answer 9

min is 8

Answer 10

thanks guys! i appreciate your help :D

Answer 11

yw