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Math Help - Proving that an inequality holds

  1. #1
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    Proving that an inequality holds

    Hello,
    I do not know if this is the right place to post this question, but I believe it falls under algebra. Please redirect me if appropriate.


    Question:


    How can I show that $$P-QR^3<\frac{R^4}{C}$$ for $$C,P,Q,R > 0?$$


    Thanks.
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  2. #2
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    Re: Proving that an inequality holds

    Quote Originally Posted by abscissa View Post
    Hello,
    I do not know if this is the right place to post this question, but I believe it falls under algebra. Please redirect me if appropriate.


    Question:


    How can I show that $$P-QR^3<\frac{R^4}{C}$$ for $$C,P,Q,R > 0?$$


    Thanks.
    You cannot show it because it is not true.

    Example. Let R = 2, C = 4, P = 100, Q = 3

    $P - QR^3 = 100 - 3 * 2^3 = 100 - 3 * 8 = 100 - 24 = 76.\ And\ \dfrac{R^4}{C} = \dfrac{2^4}{4} = \dfrac{16}{4} = 4.$

    $76 \not < 4.$

    There must be additional constraints that you have not specified.
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  3. #3
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    Re: Proving that an inequality holds

    Quote Originally Posted by JeffM View Post
    You cannot show it because it is not true.

    Example. Let R = 2, C = 4, P = 100, Q = 3

    $P - QR^3 = 100 - 3 * 2^3 = 100 - 3 * 8 = 100 - 24 = 76.\ And\ \dfrac{R^4}{C} = \dfrac{2^4}{4} = \dfrac{16}{4} = 4.$

    $76 \not < 4.$

    There must be additional constraints that you have not specified.
    Ok. You are right. Would you mind if I start a new question within this one, one with more context and details? Thanks.
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  4. #4
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    Re: Proving that an inequality holds

    Not a problem. Go right ahead. Someone will be around to help
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