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Question Number 209986 by a.lgnaoui last updated on 28/Jul/24

$$\mathrm{Solve}$$$${\mathbf{ax}}^3-\mathbf{bx}\sqrt{\mathbf{x}}+\mathbf{c}=0$$$$(\mathbf{a},\mathbf{b},\mathbf{c})\in {\mathbb{R}}^3\mathrm{and}\mathbf{x}\in \mathbb{R}$$$$(\mathit{t}\mathit{h}\mathit{e}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathit{o}\mathit{f}\mathit{x}\mathit{f}\mathit{o}\mathit{r}\mathit{a}=1,\mathit{b}=9,\mathit{c}=8)$$

Answered by mr W last updated on 28/Jul/24

$$lett=x\sqrt{x}$$$${at}^2-bt+c=0$$$$\Rightarrow t=\frac{b\pm \sqrt{b^2-4ac}}{2a}$$$$\Rightarrow x=t^{\frac{2}{3}}={\left(\frac{b\pm \sqrt{b^2-4ac}}{2a}\right)}^{\frac{2}{3}}$$

Commented by a.lgnaoui last updated on 28/Jul/24

$$\mathrm{thanks}$$

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