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Math Help - Inequality challenge questions

  1. #1
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    Inequality challenge questions

    1. Let prove that

    2. Let with . Find the minimum value of

    3. Let . Prove that
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  2. #2
    MHF Contributor

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    In what sense are these "challenge questions"?
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  3. #3
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    In the sense that they are for me
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  4. #4
    Senior Member Shanks's Avatar
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    the first and the third inequality can be easily proved by using Cauchy inequality.
    By let x+y=r, y+z=t, z+x=s; then the second inequality can be easily proved by using the Mean value inequality!
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  5. #5
    Senior Member Shanks's Avatar
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    You should try your best before asking help in the forum.
    And tell us where you are stuck on!
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