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ISI 2019 | PCB Mathematics | Question: 22

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If $\alpha, \beta, \gamma$ are the roots of the equation $x^{3}+6 x+1=0$, then prove that $$ \frac{\alpha}{\beta}+\frac{\beta}{\alpha}+\frac{\beta}{\gamma}+\frac{\gamma}{\beta}+\frac{\gamma}{\alpha}+\frac{\alpha}{\gamma}=-3. $$
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