Minimize 3x+4y+12z subject to xyz=1 using AM-GM inequality

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Homework Statement


Use the Arithmetic-Geometric Mean Inequality to minimize 3x+4y+12z to xyz=1 and x,y,z>0.

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The Attempt at a Solution


 

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What is the "Arithmetic-Geometric Mean Inequality"?

And does "minimize 3x+4y+12z to xyz=1" mean to minimize 3x+ 4y+ 12z with the condition that xyz= 1?