A) \[2\]
B) \[3\]
C) \[4\]
D) \[5\]
Correct Answer: C
Solution :
Since, \[\alpha ,\,\,\beta ,\,\,\gamma \] are the roots of the equation\[{{x}^{3}}+4x+1=0\], then \[\alpha +\beta +\gamma =0,\,\,\alpha \beta +\beta \gamma +\gamma \alpha =4\]and\[\alpha \beta \gamma =-1\] \[\therefore \] \[\frac{1}{\alpha +\beta }+\frac{1}{\beta +\gamma }+\frac{1}{\gamma +\alpha }=-\frac{1}{\gamma }-\frac{1}{\alpha }-\frac{1}{\beta }\] \[(\because \,\,\alpha +\beta +\gamma =0)\]
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