A) 0
B) \[-\frac{280\sqrt{3}}{243}\]
C) \[+\frac{280\sqrt{3}}{243}\]
D) \[\frac{280}{243}\]
Correct Answer: C
Solution :
(c): Product of the roots\[\alpha +\beta =-\frac{c}{a}=-\frac{-3}{2};\] Now\[=\frac{1}{{{\alpha }^{3}}}+\frac{1}{{{\beta }^{3}}}=\frac{{{\alpha }^{3}}+{{\beta }^{3}}}{{{(\alpha \beta )}^{3}}}\] \[=\frac{(\alpha +\beta )\left[ {{\{\alpha +\beta \}}^{2}}-3\alpha \beta \right]}{{{(\alpha \beta )}^{3}}}\] \[\frac{=\frac{-2}{\sqrt{3}}\times \left[ \frac{4}{3}+\frac{9}{2} \right]}{{{\left( \frac{-27}{8} \right)}^{=\,\frac{280\sqrt{3}}{243}}}}\]
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