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Math Help - Completing the square/Quadratics

  1. #1
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    Completing the square/Quadratics

    Find the positive constant a and b such that x^4+9/x^4 = (x^2-a/x^2)^2 + b for all non-zero values of x.

    Hence write down or obtain otherwise, the least possible value of x^4+9/x^4 for real values of x.

    Please show a step by step approach to the problem. Thanks
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  2. #2
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    Quote Originally Posted by umeirhuss View Post
    Find the positive constant a and b such that x^4+9/x^4 = (x^2-a/x^2)^2 + b for all non-zero values of x.

    Hence write down or obtain otherwise, the least possible value of x^4+9/x^4 for real values of x.

    Please show a step by step approach to the problem. Thanks
    Have you tried expanding the RHS and see how it can be compared to be the LHS?
    Last edited by mathaddict; September 25th 2010 at 05:06 AM.
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  3. #3
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    in other words, what is (x^2- a/x^2)^2? How does that differ from (x^4+ 9/x^4)?
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  4. #4
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    i try to but i got stuck and don't know where to go... i got a=3 but no answer for b!! I guess I'm doing something wrong. your help will be much appreciated. Thanks
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  5. #5
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    Quote Originally Posted by HallsofIvy View Post
    in other words, what is (x^2- a/x^2)^2? How does that differ from (x^4+ 9/x^4)?
    what about the value of b?
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