question_answer

If \[\sqrt{\mathbf{x}}\mathbf{=}{{\mathbf{a}}^{\mathbf{1/3}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{-1/3}}}\] and \[\sqrt{\mathbf{y}}\mathbf{=}{{\mathbf{a}}^{\mathbf{1/3}}}\mathbf{-}{{\mathbf{a}}^{\mathbf{-1/3}}}\], then find the value of \[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-}{{\mathbf{y}}^{\mathbf{2}}}\]

A)  \[2({{a}^{2/3}}+{{a}^{-2/3}})\]                                           

B)  \[4({{a}^{1/3}}+{{a}^{-1/3}})\]

C)  \[8({{a}^{2/3}}+{{a}^{-2/3}})\]       

D)  \[16({{a}^{1/3}}+{{a}^{-1/3}})\]

E)  None of these