A) \[\frac{-539}{192\sqrt{3}}\]
B) \[\frac{539}{192\sqrt{3}}\]
C) \[\frac{539\sqrt{3}}{192}\]
D) \[\frac{-539\sqrt{3}}{192}\]
Correct Answer: B
Solution :
| \[{{\alpha }^{3}}-{{\beta }^{3}}=(\alpha -\beta )\,\,({{\alpha }^{2}}+\alpha \beta +{{\beta }^{2}})\] |
| \[=\left( \frac{-2}{\sqrt{3}}-\frac{\sqrt{3}}{4} \right)\,\,\left( \frac{4}{3}-\frac{1}{2}+\frac{3}{16} \right)\] |
| \[=\left( \frac{-8-3}{4\sqrt{3}} \right)\times \frac{49}{48}\] |
| \[=\frac{-539}{192\sqrt{3}}\] |
| So, option [b] is correct. |
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