Find three positive integers x, y, and z that satisfy the given conditions. the sum is 48, and the sum of the squares is a minimum.

Step-by-step explanation:

Given that x+y+z = 48

Sum of squares

is minimum

Let us eliminate one variable say z = 48-x-y

f(x,y) =

Use partial derivatives to find min of f

Equate I derivative to 0

2x+6y =96 and 6x+2y = 96

Solving we get

x=y =12

z=48-24 = 24

so minimum when x=y =12 and z = 24

the answer

b. they are parallel and will never intersect.