Question

Let x, y, z be positive real numbers such that x + y + z = 12 and x³y⁴z⁵ = (0.1)(600)³. Then, x³ + y³ + z³ is equal to

(A) 342 

(B) 216 

(C) 258 

(D) 270

Answer 1

Correct option   (B) 216

We have

x + y + z = 12

By using weight arithmetic inequality

Therefore,

3k + 4k + 5k = 12

⇒ k = 1

So x = 3; y = 4; z = 5

Hence,

x³ + y³ + z³ = 27 + 64 + 125 = 216