If a + b + c = 3 where a , b , c 0 , then the greatest value of a 2 b 3 c 2 is

Question

If a + b + c = 3 where a , b , c > 0 , then the greatest value of a 2 b 3 c 2 is, 3 10 2 4 7 7, 3 9 2 4 7 7, 3 8 2 4 7 7, 3 9 2 3 7 6

MARKS App · Accepted Answer

Given, a + b + c = 3 ⇒ 2 ⋅ a 2 + 3 ⋅ b 3 + 2 ⋅ c 2 = 3 a 2 + a 2 + b 3 + b 3 + b 3 + c 2 + c 2 7 ≥ a 2 2 b 3 3 c 2 2 1 7 a + b + c 7 ≥ a 2 b 3 c 2 2 4 3 3 1 7 3 7 7 ≥ a 2 b 3 c 2 2 4 3 3 ⇒ a 2 b 3 c 2 ≤ 3 7 7 7 × 2 4 × 3 3 = 2 4 × 3 10 7 7 Hence, maximum value = 2 4 × 3 10 7 7

Search any question & find its solution

Looking for more such questions to practice?