If , be real numbers such that x^3 - x^2 + x - 6 = 0 has its roots real and positive then the minimum value of is

JEE Advanced Mathematics question

If be real numbers such that has its roots real and positive then the minimum value of is

Answer: (A)

Let the roots be . By Vieta's formulas, and . Apply AM ≥ GM to the three positive numbers :

{(ab)(bc)(ca)

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Question ID VK-109413