Equations And Inequalities Question 35
Question: If $ {{(\sqrt{2})}^{x}}+{{(\sqrt{3})}^{x}}={{(\sqrt{13})}^{x/2}}, $ then the number of values of x is
Options:
A) 2
B) 4
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ {2^{x/2}}+{3^{x/2}}={{(\sqrt{13})}^{x/2}} $
$ \Rightarrow {{( \frac{2}{\sqrt{13}} )}^{x/2}}+{{( \frac{3}{\sqrt{13}} )}^{x/2}}=1 $ Which is of the form $ {{\cos }^{x/2}}\alpha +{{\sin }^{x/2}}\alpha =1. $
$ \therefore ,\frac{x}{2}=2. $
BETA
