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Let x, y, and z be positive real numbers. Find the minimum value of \((x + 2y + 4z) \left( \frac{4}{x} + \frac{2}{y} + \frac{1}{z} \right)\).

Btw. I have to use the AM-GM inequality thingy. Help :)

 May 26, 2021
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You get the minimum value when x = y = z = 1: (x + 2y + 4z)(4/x + 2/y + 1/z) = 49.

 May 26, 2021

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