- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
If $ x+\frac{1}{x}=11 $, find the value of $ x^{2}+\frac{1}{x^{2}} $.
Given:
\( x+\frac{1}{x}=11 \)
To do:
We have to find the value of \( x^{2}+\frac{1}{x^{2}} \).
Solution:
We know that,
$(a+b)^2=a^2+b^2+2ab$
$(a-b)^2=a^2+b^2-2ab$
$(a+b)(a-b)=a^2-b^2$
Therefore,
$x+\frac{1}{x}=11$
Squaring both sides, we get,
$(x+\frac{1}{x})^{2}=(11)^{2}$
$\Rightarrow x^{2}+\frac{1}{x^{2}}+2\times x \times \frac{1}{x}=121$
$\Rightarrow x^{2}+\frac{1}{x^{2}}=121-2$
$\Rightarrow x^{2}+\frac{1}{x^{2}}=119$
The value of \( x^{2}+\frac{1}{x^{2}} \) is 119.
Advertisements