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Math Help - Geometric Mean < Arithmetic Mean using MVT

  1. #1
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    Geometric Mean < Arithmetic Mean using MVT

    I am attempting to prove that the geometric mean of two numbers is always less than or equal to the arithmetic mean of those two numbers. I want to use the MVT to do this proof, but where do I start?

    I know to use the square root function, but what interval do I need to use the MVT on? How do I do this proof?
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  2. #2
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    Re: Geometric Mean < Arithmetic Mean using MVT

    Hey zachd77.

    Can you show that (x1 + x2 + ... + xn)^n <= (x1*x2*...*xn) by a multinomial argument?
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