Let x, y, z be positive real numbers such that x+y+z = 12 and x^3y^4z^5 = (0.1)(600)^3. Then x^3+y^3+z^3 is equal to

JEE Main 2016 Mathematics question

Let , , be positive real numbers such that and . Then is equal to

Answer: (2)

First evaluate the product: . Now apply the AM-GM inequality to twelve quantities — the number taken three times, four times and five times:

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Question ID VK-115557