A) 2
B) 4
C) 1
D) None of these
Correct Answer: C
Solution :
[c] \[{{2}^{x/2}}+{{3}^{x/2}}={{(\sqrt{13})}^{x/2}}\] \[\Rightarrow {{\left( \frac{2}{\sqrt{13}} \right)}^{x/2}}+{{\left( \frac{3}{\sqrt{13}} \right)}^{x/2}}=1\] Which is of the form \[{{\cos }^{x/2}}\alpha +{{\sin }^{x/2}}\alpha =1.\] \[\therefore \,\,\,\,\,\frac{x}{2}=2.\]
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