![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
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 $x – y = 7$ and $xy = 9$, find the value of $x^2+y^2$.
Given:
$x – y = 7$ and $xy = 9$
To do:
We have to find the value of $x^2+y^2$.
Solution:
The given expressions are $x – y = 7$ and $xy = 9$. Here, we have to find the value of $x^2 + y^2$. So, by squaring the given expression and using the identity $(a-b)^2=a^2-2ab+b^2$, we can find the required value.
$xy = 9$............(i)
$(a-b)^2=a^2-2ab+b^2$.............(ii)
Now,
$x – y = 7$
Squaring on both sides, we get,
$(x – y)^2 = 7^2$ [Using (ii)]
$x^2-2xy+y^2=49$
$x^2-2(9)+y^2=49$ [Using (i)]
$x^2-18+y^2=49$
$x^2+y^2=49+18$ (Transposing $-18$ to RHS)
$x^2+y^2=67$
Hence, the value of $x^2+y^2$ is $67$.
Advertisements