The minimum value of the sum of real numbers a^ -5 , a^ -4 , 3a^ -3 , 1, a^8 and a^ 10 with a > 0 is

JEE Advanced 2011 Mathematics question

The minimum value of the sum of real numbers , , , 1, and with is

Answer: 8

Split into three equal terms and apply AM ≥ GM to the eight positive numbers : $

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Question ID VK-025942