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Question Number 96530 by abony1303 last updated on 02/Jun/20

$$\mathbf{If}:{(1+m)}^3-3m^3=20⩽m⩽1$$$$\mathbf{Find}:{(1+m)}^2-3m^2$$

Commented by MJS last updated on 02/Jun/20

$$\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{think}{\mathrm{there}}^{\prime }\mathrm{s}\mathrm{a}‘‘{\mathrm{nice}}^{″}\mathrm{solution}$$$$m=\frac{1}{2}-\sqrt{3}\sin \frac{\arcsin \frac{2\sqrt{3}}{9}}{3}$$$$\Rightarrow$$$${(1+m)}^2-3m^2=-\frac{3}{2}+3\cos \frac{2\arcsin \frac{2\sqrt{3}}{9}}{3}$$

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