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djymndl07
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I was going through an article. I have the following functions,
$$f(\text{r})\text{=}-\frac{2 M r^2}{g^3+r^3}+\frac{8}{3} \pi P r^2+1$$
$$\text{v}(\text{r})\text{=}\frac{f(r)}{r^2}$$
Now I want to solve v'[r]=0 for r. Clearly This cannot be solved analytically. But there they solved it somehow and got the following result.
$$\text{r}=\sqrt[3]{-g^3+\sqrt{g^6-2 g^3 M^3}+M^3}+\frac{M^2}{\sqrt[3]{-g^3+\sqrt{g^6-2 g^3 M^3}+M^3}}+M$$
Can anyone tell me how can it be solved in mathematica or what method did they use?
Thanks in advance.
$$f(\text{r})\text{=}-\frac{2 M r^2}{g^3+r^3}+\frac{8}{3} \pi P r^2+1$$
$$\text{v}(\text{r})\text{=}\frac{f(r)}{r^2}$$
Now I want to solve v'[r]=0 for r. Clearly This cannot be solved analytically. But there they solved it somehow and got the following result.
$$\text{r}=\sqrt[3]{-g^3+\sqrt{g^6-2 g^3 M^3}+M^3}+\frac{M^2}{\sqrt[3]{-g^3+\sqrt{g^6-2 g^3 M^3}+M^3}}+M$$
Can anyone tell me how can it be solved in mathematica or what method did they use?
Thanks in advance.
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