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JEE Main & Advanced Sample Paper JEE Main Sample Paper-5

  • question_answer
    \[\alpha \]and \[\beta \]are cube roots of unity, then \[{{\alpha }^{4}}+{{\beta }^{4}}+{{\alpha }^{-1}}{{\beta }^{-1}}\]is equal to

    A)  1                                            

    B)  0                    

    C)  -1                                          

    D)  None of these

    Correct Answer: B

    Solution :

     \[\because \]\[\alpha \] and \[\beta \] are cube roots of unity \[\therefore \]                  \[\alpha =\omega ,\beta ={{\omega }^{2}}\] \[{{\alpha }^{4}}+{{\beta }^{4}}+{{\alpha }^{-1}}{{\beta }^{-1}}={{\omega }^{4}}+{{\omega }^{8}}+\frac{1}{\omega }.\frac{1}{{{\omega }^{2}}}\] \[={{\omega }^{3+1}}+{{\omega }^{6+2}}+1=1+\omega +{{\omega }^{2}}=0\]


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