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If $\alpha$ and $\beta$ are the roots of $x^{2}+4 x+6=0$, then what is the
value of $\alpha^{3}+\beta^{3} ?$
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value of $\alpha^{3}+\beta^{3} ?$
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The correct answer is:
8
$\alpha$ and $\beta$ are theroots of $x^{2}+4 x+6=0$ $\therefore \alpha+\beta=-4$ and $\alpha \beta=6$
Now, $\alpha^{3}+\beta^{3}=(\alpha+\beta)^{3}-3 \alpha \beta(\alpha+\beta)$
$=(-4)^{3}-3 \times 6(-4)=-64+72=8$
Now, $\alpha^{3}+\beta^{3}=(\alpha+\beta)^{3}-3 \alpha \beta(\alpha+\beta)$
$=(-4)^{3}-3 \times 6(-4)=-64+72=8$
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