If a , b , c ∈ R + such that a + b + c = 27 , then the maximum value of a 2 b 3 c 4 is equal to

Step-by-step solution

Consider nine numbers a 2 , a 2 , b 3 , b 3 , b 3 , c 4 , c 4 , c 4 , c 4 Using A M ≥ G M , we get, a 2 + a 2 + b 3 + b 3 + b 3 + c 4 + c 4 + c 4 + c 4 9 ≥ a 2 2 b 3 3 c 4 4 1 9 ⇒ a + b + c 9 ≥ a 2 b 3 c 4 2 2 3 3 4 4 1 9 ⇒ 27 9 9 ≥ a 2 b 3 c 4 2 2 3 3 2 8 ⇒ a 2 b 3 c 4 ≤ 2 10 ⋅ 3 12