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Question Number 101085 by ajfour last updated on 30/Jun/20

Commented by ajfour last updated on 30/Jun/20

$$xintermsofbandc,givenany$$$$realbandc.$$$$(whatseemsarightangleis$$$$indeedarightangle)$$

Answered by 1549442205 last updated on 07/Jul/20

$$\mathrm{From}\mathrm{the}\mathrm{figure}\mathrm{we}\mathrm{have}:\frac{\mathrm{c}}{{\mathrm{x}}^2}+\frac{\mathrm{b}}{\mathrm{x}}=\mathrm{x}$$$$\iff {\mathrm{x}}^3-\mathrm{bx}-\mathrm{c}=0(\ast )$$$$\Rightarrow \mathrm{x}={}^3\sqrt{\frac{\mathbf{c}+\sqrt{{\mathbf{c}}^2-\frac{4{\mathbf{b}}^3}{27}}}{2}}+{}^3\sqrt{\frac{\mathbf{c}-\sqrt{{\mathbf{c}}^2-\frac{4{\mathbf{b}}^3}{27}}}{2}}$$$$(\mathbf{see}\mathbf{solution}\mathbf{in}\mathbf{question}100146$$$$\mathbf{above}\mathbf{the}\mathbf{equation}(\ast ))$$

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