- #1
i13m
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Hi, all
After I differentiate a mathematical model, I got the following equation.
I wonder whether or not it is possible to solve c with the following equation
[tex] 0=c^3\,\left(\ifrac{3\,\left(A^2+c\,A\right)^{\frac{4}{3}}}{c^{\frac{8}{3}}}-\ifrac{24\,\left(A^2+c\,A\right)^{\frac{2}{3}}}{c^{\frac{4}{3}}}+20\right)+c\,\left(-\ifrac{12\,A^2\,\left(A^2+c\,A\right)^{\frac{2}{3}}}{c^{\frac{4}{3}}}-\ifrac{4\,A^2\,\left(A^2+c\,A\right)^{\frac{1}{3}}}{c^{\frac{2}{3}}}\right)+c^5\,\left(\ifrac{72\,\left(A^2+c\,A\right)^{\frac{2}{3}}}{c^{\frac{4}{3}}}-44\right)+c^2\,\left(9\,A-\ifrac{2\,A\,\left(A^2+c\,A\right)^{\frac{1}{3}}}{c^{\frac{2}{3}}}\right)+7\,A^3-40\,c^4\,A[/tex]
where A will be a possible integer
Can it be done analytically, or the numerical method is a possible solution.
Thanks
Homework Statement
After I differentiate a mathematical model, I got the following equation.
I wonder whether or not it is possible to solve c with the following equation
[tex] 0=c^3\,\left(\ifrac{3\,\left(A^2+c\,A\right)^{\frac{4}{3}}}{c^{\frac{8}{3}}}-\ifrac{24\,\left(A^2+c\,A\right)^{\frac{2}{3}}}{c^{\frac{4}{3}}}+20\right)+c\,\left(-\ifrac{12\,A^2\,\left(A^2+c\,A\right)^{\frac{2}{3}}}{c^{\frac{4}{3}}}-\ifrac{4\,A^2\,\left(A^2+c\,A\right)^{\frac{1}{3}}}{c^{\frac{2}{3}}}\right)+c^5\,\left(\ifrac{72\,\left(A^2+c\,A\right)^{\frac{2}{3}}}{c^{\frac{4}{3}}}-44\right)+c^2\,\left(9\,A-\ifrac{2\,A\,\left(A^2+c\,A\right)^{\frac{1}{3}}}{c^{\frac{2}{3}}}\right)+7\,A^3-40\,c^4\,A[/tex]
where A will be a possible integer
Can it be done analytically, or the numerical method is a possible solution.
Homework Equations
The Attempt at a Solution
Thanks