Quantitative Aptitude Ques 1267

Question: If $ a=\frac{\sqrt{3}+1}{\sqrt{3}-1} $ and $ b=\frac{\sqrt{3}-1}{\sqrt{3}+1}, $ the value of $ ( \frac{a^{2}+ab+b^{2}}{a^{2}-ab+b^{2}} ) $ is

Options:

A) $ \frac{15}{13} $

B) $ \frac{16}{13} $

C) $ \frac{11}{13} $

D) $ \frac{12}{13} $

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ a=\frac{(\sqrt{3}+1)}{(\sqrt{3}-1)}\times \frac{(\sqrt{3}+1)}{(\sqrt{3}+1)}=\frac{{{(\sqrt{3}+1)}^{2}}}{{{(\sqrt{3})}^{2}}-{{(1)}^{2}}} $ [by rationalisation] $ =\frac{3+1+2\sqrt{3}}{3-1}=\frac{4+2\sqrt{3}}{2}=2+\sqrt{3} $ $ a^{2}={{(2+\sqrt{3})}^{2}}=4+3+4\sqrt{3}=(7+4\sqrt{3}) $ $ b^{2}={{(2-\sqrt{3})}^{2}}=4+3-4\sqrt{3}=(7-4\sqrt{3}) $ $ ab=\frac{(\sqrt{3}+1)}{(\sqrt{3}-1)}\times \frac{(\sqrt{3}-1)}{(\sqrt{3}+1)}=1 $ Now, $ \frac{a^{2}+ab+b^{2}}{a^{2}-ab+b^{2}}=\frac{a^{2}+b^{2}+ab}{a^{2}+b^{2}-ab} $ $ =\frac{(7+4\sqrt{3})+(7-4\sqrt{3})+1}{(7+4\sqrt{3})+(7-4\sqrt{3})-1}=\frac{15}{13} $
Bank Preparation

IBPS Clerk

IBPS PO

IBPS Office Assistants

IBPS RRB Officers

IBPS SO

Bank Courses

All Courses

Recorded Course for English

Recorded Course for Reasoning

Recorded Course for Mathematics

NCERT Books

Class 11

Class 12

Important Resources

Banking Awareness

Financial Awareness

Economics

Blog

Forum

SATHEE Forums

icon  BETA

© 2025 Copyright SATHEE

Privacy Policy

Powered by Prutor@IITK

sathee@iitk.ac.in
Media coverage of SATHEE
goolge

Play Store
goolge

App Store
The Ministry of Education has launched the SATHEE initiative in association with IIT Kanpur to provide free guidance for competitive exams. SATHEE offers a range of resources, including reference video lectures, mock tests, and other resources to support your preparation. Please note that participation in the SATHEE program does not guarantee clearing any exam or admission to any institute.