Question : The value of $\frac{1}{1+\sqrt{2}+\sqrt{3}}+\frac{1}{1-\sqrt{2}+\sqrt{3}}$ is:
Option 1: $\sqrt{2}$
Option 2: $\sqrt{3}$
Option 3: $1$
Option 4: $4(\sqrt{3}+\sqrt{2})$
New: SSC CHSL tier 1 answer key 2024 out | 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: $1$
Solution :
$\frac{1}{1+\sqrt{2}+\sqrt{3}}+\frac{1}{1-\sqrt{2}+\sqrt{3}}$
$= \frac{1}{(1+\sqrt{3})+\sqrt{2}}+\frac{1}{(1+\sqrt{3})-\sqrt{2}}$
$= \frac{1+\sqrt{3}-\sqrt{2}+1+\sqrt{3}+\sqrt{2}}{[(1+\sqrt{3})+\sqrt{2}][(1+\sqrt{3})-\sqrt{2}]}$
$= \frac{2\sqrt{3}+2}{(1+\sqrt{3})^{2}-(\sqrt{2})^{2}}$
$= \frac{2\sqrt{3}+2}{1+3+2\sqrt{3}-2}$
$= \frac{2\sqrt{3}+2}{2\sqrt{3}+2}$
$=1$
Hence, the correct answer is $1$.
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 “”.
