Complex Numbers And Quadratic Equations question 743
Question: If $ {\log_2}x+{\log_{x}}2=\frac{10}{3}={\log_2}y+{\log_{y}}2 $ and $ x\ne y, $ then $ x+y= $ [EAMCET 1994]
Options:
A) 2
B) 65/8
C) 37/6
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
We have $ {\log_2}x+\frac{1}{{\log_2}x}=3+\frac{1}{3}={\log_2}y+\frac{1}{{\log_2}y} $ \ $ {\log_2}x=3,{\log_2}y=\frac{1}{3} $ $ (\because x\ne y) $
Þ $ x=2^{3} $ and $ y={2^{1/3}}\Rightarrow x+y=8+{2^{1/3}} $ .
BETA
