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Question Number 211881 by Spillover last updated on 23/Sep/24

Answered by som(math1967) last updated on 23/Sep/24

$$\alpha +\beta +\gamma =1,\alpha \beta +\beta \gamma +\gamma \alpha =-2$$$$\alpha \beta \gamma =-1$$$${\alpha }^2+{\beta }^2+{\gamma }^2=1+4=5$$$${}^3\sqrt{\frac{{\alpha }^6}{{\alpha }^2{\beta }^2{\gamma }^2}}{+}^3\sqrt{\frac{{\beta }^6}{{\alpha }^2{\beta }^2{\gamma }^2}}{+}^3\sqrt{\frac{{\gamma }^6}{{\alpha }^2{\beta }^2{\gamma }^2}}$$$$=\frac{{\alpha }^2}{1}+\frac{{\beta }^2}{1}+\frac{{\gamma }^2}{1}$$$$=({\alpha }^2+{\beta }^2+{\gamma }^2)=5$$

Commented by Spillover last updated on 23/Sep/24

$$correct.thanks$$

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