Sequence And Series Question 337
Question: If $ a=1+(\sqrt{3}-1)+{{(\sqrt{3}-1)}^{2}}+{{(\sqrt{3}-1)}^{3}}+…. $ and $ ab=1 $ , then a and bare the roots of the equation
Options:
A) $ x^{2}+4x-1=0 $
B)
C) $ x^{2}+4x+1=0 $
D) $ x^{2}-4x+1=0 $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ a=\frac{1}{1-( \sqrt{3}-1 )}=\frac{1}{2-\sqrt{3}}=2+\sqrt{3} $ and $ ab=1\Rightarrow b=2-\sqrt{3} $ so, a and b are roots of $ x^{2}-4x+1=0 $
BETA
