- Trending Categories
- 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

# The sum of two numbers is 1000 and the difference between their square is 256000. Find the numbers.

Given:

The sum of two numbers is 1000 and the difference between their square is 256000.

To do:

We have to find the numbers.

Solution:

Let one of the numbers be $x$.

This implies,

The other number $=1000-x$.

According to the question,

$x^2-(1000-x)^2=256000$ or $(1000-x)^2-x^2=256000$

$x^2-(1000000+x^2-2\times1000x)=256000$ or $1000000+x^2-2\times1000x-x^2=256000$

$x^2-x^2-1000000+2000x=256000$ or $x^2-x^2+1000000-2000x=256000$

$2000x=256000+1000000$ or $2000x=1000000-256000$

$2000x=1256000$ or $2000x=744000$

$x=\frac{1256000}{2000}$ or $x=\frac{744000}{2000}$

$x=628$ or $x=372$

This implies,

$1000-x=1000-628=372$ or $1000-372=628$

Therefore, the two numbers are $372$ and $628$.

Advertisements