Find three positive integers x y and z that satisfy the give

Find three positive integers x, y, and z that satisfy the given conditions.

The product is 8, and the sum is a minimum.

0/2 points | Previous Answers LarCalc10 13.9.005 Find three positive integers x, y, and z that satisfy the given conditions. The product is 8, and the sum is a minimum. (x, y, z) = ( | 2

Solution

Conditions satisfied by the integers are:

1. x>0,y>0.z>0

2. xyz=8

xyz=8 and all are integers hence all positive values of x,y,z must be less than 8 and greater than 1

Sum,S=x+y+z

Problem is symmetric in x,y,z ie if x=a,y=b,z=c is a solution.

Then, x=c,y=a,z=b is also a solution and any other permutation of a,b,c

Because:xyz=abc=8,x+y+z=a+b+c

Hence, a=b=c

But abc=8=a*a*a

Hence, a=2

Minimum sum is: 2+2+2=6

(x,y,z)=(2,2,2)