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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- May 23rd 2011, 03:54 AMdbeckerSolve 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 - May 23rd 2011, 04:05 AMchisigma
With the substitution $\displaystyle \alpha= \sqrt{x}$ the equation becomes...

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

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

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$ - May 23rd 2011, 05:06 AMdbecker
Thank you! Now it's just obvious (Wink)

Regards,

Daniel