question_answer

If \[x=\frac{\sqrt{8}+\sqrt{2}}{2}\]  and \[y=\frac{\sqrt{8}-\sqrt{2}}{2},\] then the value of \[{{\log }_{121}}\,({{x}^{2}}+4xy+{{y}^{2}})\] is equal to ______.

A)  1                                

B)  \[\frac{1}{2}\]

C)  \[\frac{13}{4}\]                        

D)  2

E)  None of these