- 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
Find the value of $4x^2 + y^2 + 25z^2 + 4xy - 10yz - 20zx$ when $x = 4, y = 3$ and $z = 2$.
Given:
$x = 4, y = 3$ and $z = 2$.
To do:
We have to find the value of $4x^2 + y^2 + 25z^2 + 4xy - 10yz - 20zx$.
Solution:
We know that,
$(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$
Therefore,
$4x^2 + y^2 + 25z^2 + 4xy - 10yz - 20zx = (2x)^2 + (y)^2 + (5z)^2 + 2 \times 2x \times y-2 \times y \times 5z - 2 \times 5z \times 2x$
$= (2x + y- 5z)^2$
$= (2 \times 4 + 3- 5 \times 2)^2$
$= (8 + 3- 10)^2$
$= (11 - 10)^2$
$= 1^2$
$= 1$
Hence, the value of $4x^2 + y^2 + 25z^2 + 4xy - 10yz - 20zx$ is $1$.
Advertisements