A) 1
B) 2
C) 4
D) infinite
Correct Answer: B
Solution :
\[{{2}^{x/2}}+{{(\sqrt{2}+1)}^{x}}={{(5+2\sqrt{2})}^{x/2}}\] \[\therefore \]\[{{\left( \frac{\sqrt{2}}{\sqrt{5+2\sqrt{2}}} \right)}^{x}}+{{\left( \frac{\sqrt{2}+1}{\sqrt{5+2\sqrt{2}}} \right)}^{x}}=1\] Let\[\cos x=\frac{\sqrt{2}}{\sqrt{5+2\sqrt{2}},}\]then\[\sin x=\frac{\sqrt{2}+1}{\sqrt{5+2\sqrt{2}}}\] \[\therefore \]\[{{\cos }^{x}}\alpha +{{\sin }^{x}}\alpha =1\]\[\Rightarrow \]\[z=2\]
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