question_answer

If \[x=\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}},\,y=\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}},\] then \[3{{x}^{2}}+4xy-3{{y}^{2}}=\]

A)  \[\frac{1}{3}\,\,[56\,\sqrt{10}-12]\]        

B)  \[\frac{1}{3}\,\,[56\,\sqrt{10}+12]\]

C)  \[\frac{1}{3}\,\,[56+12\,\sqrt{10}]\]       

D)  \[\frac{1}{5}\,\,[56+10\,\sqrt{15}]\]

E)  None of these