question_answer

If \[\mathbf{x=}{{\mathbf{p}}^{\mathbf{1/3}}}\mathbf{+}{{\mathbf{p}}^{\mathbf{-}}}^{\mathbf{1/3}}\] and \[\mathbf{y=}{{\mathbf{p}}^{\mathbf{1/3}}}\mathbf{-}{{\mathbf{p}}^{\mathbf{-}}}^{\mathbf{1/3}}\], then find the value of \[\frac{{{\mathbf{(}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{)}}^{\mathbf{3}}}}{\mathbf{(}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{+xy)(}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{-xy)}}\]

A)  1                                                                    

B)  2

C)  3                                                                    

D)  4

E)  None of these