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Thread: equation

  1. #1 equation 
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    given that 0<x<1/2 solve the equation 2x√(1-x^2)+x√(1-4x^2) = 1


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  3. #2  
    Forum Bachelors Degree Demen Tolden's Avatar
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    square twice.






    The most important thing I have learned about the internet is that it needs lot more kindness and patience.
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  4. #3 Re: equation 
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    Quote Originally Posted by siegfried
    given that solve the equation
    By Cauchy–Schwarz, .

    We have equality if and only if . Solve that for x.
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  5. #4  
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    how do you use cauchy-schwarz
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  6. #5  
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    The general Cauchy–Schwarz inequality states that for all , with equality holding if and only if and are linearly dependent in .

    Hence, if are positive real numbers, and .

    So, for your problem, if you take , , , ) you have



    and :wink:
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