Complex Numbers And Quadratic Equations question 742
Question: If $ x=\sqrt{7+4\sqrt{3}}, $ then $ x+\frac{1}{x}= $ [EAMCET 1994]
Options:
A) 4
B) 6
C) 3
D) 2
Show Answer
Answer:
Correct Answer: A
Solution:
We have $ x=\sqrt{7+4\sqrt{3}} $ \ $ \frac{1}{x}=\frac{1}{\sqrt{7+4\sqrt{3}}}=\frac{\sqrt{7-4\sqrt{3}}}{\sqrt{7+4\sqrt{3}}.\sqrt{7-4\sqrt{3}}} $ $ =\sqrt{7-4\sqrt{3}} $ \ $ x+\frac{1}{x}=\sqrt{7+4\sqrt{3}}+\sqrt{7-4\sqrt{3}} $ $ =(\sqrt{3}+2)+(2-\sqrt{3})=4 $ .
BETA
