A) \[-1\]
B) \[-2\]
C) 0
D) 1
E) 2
Correct Answer: E
Solution :
Given,\[2\alpha =-1-i\sqrt{3}\]and\[2\beta =-1-i\sqrt{3}\] \[\therefore \] \[\alpha +\beta =-1\] and \[\alpha \beta =1\] Now, \[5{{\alpha }^{4}}+5{{\beta }^{4}}+\frac{7}{\alpha \beta }\] \[=5[{{\{{{(\alpha +\beta )}^{2}}-2\alpha \beta \}}^{2}}-2{{(\alpha \beta )}^{2}}]+\frac{7}{\alpha \beta }\] \[=5[{{\{{{(-1)}^{2}}-2\times 1\}}^{2}}-2{{(1)}^{2}}]+\frac{7}{1}\] \[=5(1-2)+7=2\]
You need to login to perform this action.
You will be redirected in
3 sec
