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Math Help - Solve y(x)=sqrt(x)*(A+B*x)-C=0 ?

  1. #1
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    Solve y(x)=sqrt(x)*(A+B*x)-C=0 ?

    Hello everyone, I just came along the following function:

    y(x) = sqrt(x)*(A+B*x)-C=0

    x is the independent variable and A,B,C are constant numbers.

    How can we solve this function for x? Is it possible analytically?

    Thank you for your help!
    Daniel
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  2. #2
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by dbecker View Post
    Hello everyone, I just came along the following function:

    y(x) = sqrt(x)*(A+B*x)-C=0

    x is the independent variable and A,B,C are constant numbers.

    How can we solve this function for x? Is it possible analytically?

    Thank you for your help!
    Daniel
    With the substitution \alpha= \sqrt{x} the equation becomes...

     b\ \alpha^{3} + a\ \alpha -c=0 (1)

    ... the algebraic solution of which was found in Italy in the XVI-th century ...

    Kind regards

    \chi \sigma
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  3. #3
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    Thank you! Now it's just obvious

    Regards,
    Daniel
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