Question : If $a=\frac{1}{a-\sqrt{6}}$ and $(a>0)$, then the value of $\left(a+\frac{1}{a}\right)$ is:
Option 1: $\sqrt{6}$
Option 2: $\sqrt{10}$
Option 3: $\sqrt{15}$
Option 4: $\sqrt{7}$
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: $\sqrt{10}$
Solution :
$a=\frac{1}{a-\sqrt{6}}(x>0)$
$⇒a^2-a\sqrt 6-1=0$
$⇒a^2-1=a\sqrt 6$
Multiplying both sides by $\frac{1}{a}$, we get,
$⇒a-\frac{1}{a}=\sqrt 6$
Squaring both sides, we get,
$⇒(a-\frac{1}{a})^2=(\sqrt 6)^2$
$⇒a^2+\frac{1}{a^2}-2=6$
Adding 4 to both sides, we get,
$⇒a^2+\frac{1}{a^2}+2=6+4$
$⇒(a+\frac{1}{a})^2=10$
$\therefore a+\frac{1}{a}=\sqrt{10}$
Hence, the correct answer is $\sqrt{10}$.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
