A) \[\frac{53}{48}\]
B) \[\frac{59}{48}\]
C) \[\frac{73}{48}\]
D) \[\frac{71}{48}\]
Correct Answer: C
Solution :
| \[{{\alpha }^{2}}+{{\beta }^{2}}={{(\alpha +\beta )}^{2}}-2\alpha \beta \] |
| \[={{\left( \frac{-5}{4\sqrt{3}} \right)}^{2}}-2\times \left( \frac{-1}{2} \right)=\frac{25}{48}+1=\frac{73}{48}\] |
| Alternate method: |
| \[{{\alpha }^{2}}+{{\beta }^{2}}={{\left( \frac{-2}{\sqrt{3}} \right)}^{2}}+{{\left( \frac{\sqrt{3}}{4} \right)}^{2}}=\frac{4}{3}+\frac{3}{16}\] |
| \[=\frac{64+9}{48}=\frac{73}{48}\] |
| So, option [c] is correct. |
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