Question

If a+b+c = 13, then what is the maximum value of

(a - 3)( b - 2)(c + 1)

Answer 1

aritmetic mean is >= geometric mean
((a-3)+(b-2)+(c+1))/3 >= ((a-3)(b-2)(c+1))^(1/3)
((a+b+c -4)/3 )^3>= (a-3)(b-2)(c+1)
((13-4)/3)^3> = (a-3)(b-2)(c+1)
(9/3)^3> = (a-2)(b-2)(c+1)
27 >= (a-2)(b-2)(c+1)