A) \[-1/2\]
B) \[1/4\]
C) \[{{3}^{2}}\]
D) \[1/{{3}^{2}}\]
Correct Answer: B
Solution :
Since, \[\alpha \] and \[\beta \] are the roots of the equation\[{{x}^{2}}+2x+4=0\], then \[\alpha +\beta =-2\]and\[\alpha \beta =4\] \[\therefore \] \[\frac{1}{{{\alpha }^{3}}}+\frac{1}{{{\beta }^{3}}}=\frac{{{\alpha }^{3}}+{{\beta }^{3}}}{{{(\alpha \beta )}^{3}}}\] \[=\frac{{{(\alpha +\beta )}^{3}}-3\alpha \beta (\alpha +\beta )}{{{(\alpha \beta )}^{3}}}\] \[=\frac{{{(-2)}^{3}}-3(4)(-2)}{{{(4)}^{3}}}=\frac{-8+24}{64}\]\[=\frac{1}{4}\]
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