Complex Numbers And Quadratic Equations question 751
Question: A real root of the equation $ {\log_4}{{\log_2}(\sqrt{x+8}-\sqrt{x})}=0 $ is [AMU 1999]
Options:
A) 1
B) 2
C) 3
D) 4
Show Answer
Answer:
Correct Answer: A
Solution:
$ {\log_4}{ {\log_2}(\sqrt{x+8}-\sqrt{x}) }=0 $
$ \Rightarrow 4^{0}={\log_2}( \sqrt{x+8}-\sqrt{x} ) $
$ \Rightarrow 2^{1}=\sqrt{x+8}-\sqrt{x} $
$ \Rightarrow 4=x+8+x-2\sqrt{x^{2}+8x} $
$ \Rightarrow 2\sqrt{x^{2}+8x}=2x+4 $
$ \Rightarrow x^{2}+8x=x^{2}+4+4x $
$ \Rightarrow 4x=4 $
$ \Rightarrow x=1 $ .
BETA
