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Math Help - find the infimum

  1. #1
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    find the infimum

    inf{ z = x + x^(-1): x>0 }


    any help would be greatly appreciated!
    Last edited by pseudonym; November 6th 2009 at 02:02 PM.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by pseudonym View Post
    in{ z = x + x^(-1): x>0 }


    any help would be greatly appreciated!
    What percisely are you having difficulties with?
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  3. #3
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    Quote Originally Posted by pseudonym View Post
    in{ z = x + x^(-1): x>0 }
    For every a~\&~b it follows that a^2+b^2\ge 2ab..
    Equality holds only if a=b

    For your problem let a=\sqrt{x}~\&~b=\frac{1}{\sqrt{x}}.
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    Quote Originally Posted by Drexel28 View Post
    What percisely are you having difficulties with?


    my understanding is that I have to find the greatest lower bound, i.e. the smallest value of x for z to exist?
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  5. #5
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    Quote Originally Posted by pseudonym View Post
    my understanding is that I have to find the greatest lower bound, i.e. the smallest value of x for z to exist?
    Do you understand that every z in your set is such that z\ge 2?
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