If X=3,y=-4,find X²+y² And X²-y² Write One Morw Pair Number X²+y²=5²

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Introduction

Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols. It is a fundamental subject that is used in various fields such as science, engineering, economics, and computer science. In this article, we will focus on solving a simple algebra problem that involves finding the values of x²+y² and x²-y² given the values of x and y.

Given Values

We are given two values: x = 3 and y = -4. We need to find the values of x²+y² and x²-y² using these given values.

Finding x²+y²

To find x²+y², we need to square the values of x and y and then add them together. The formula for this is:

x²+y² = (x)² + (y)²

Using the given values, we can substitute x = 3 and y = -4 into the formula:

x²+y² = (3)² + (-4)² x²+y² = 9 + 16 x²+y² = 25

Finding x²-y²

To find x²-y², we need to square the values of x and y and then subtract the value of y² from the value of x². The formula for this is:

x²-y² = (x)² - (y)²

Using the given values, we can substitute x = 3 and y = -4 into the formula:

x²-y² = (3)² - (-4)² x²-y² = 9 - 16 x²-y² = -7

Another Pair of Numbers: x²+y²=5²

Now, let's consider another pair of numbers where x²+y²=5². We can find the values of x and y using the formula:

x²+y² = (x)² + (y)²

We know that x²+y²=5², so we can substitute 5² into the formula:

5² = (x)² + (y)² 25 = (x)² + (y)²

To find the values of x and y, we need to find two numbers whose squares add up to 25. One possible pair of numbers is x = 3 and y = 4, since:

(3)² + (4)² = 9 + 16 = 25

Therefore, we can conclude that x = 3 and y = 4 is one possible pair of numbers where x²+y²=5².

Conclusion

In this article, we have learned how to find the values of x²+y² and x²-y² given the values of x and y. We have also considered another pair of numbers where x²+y²=5² and found the values of x and y using the formula. Algebra is a fundamental subject that is used in various fields, and understanding the basics of algebra is essential for solving problems in mathematics and science.

Tips and Tricks

  • When solving algebra problems, it is essential to read the problem carefully and understand what is being asked.
  • Use the formulas and equations to find the values of x and y.
  • Check your work by plugging the values back into the original equation.
  • Practice, practice, practice! The more you practice, the better you will become at solving algebra problems.

Common Mistakes

  • Not reading the problem carefully and understanding what is being asked.
  • Not using the formulas and equations to find the values of x and y.
  • Not checking your work by plugging the values back into the original equation.
  • Not practicing enough to become proficient in solving algebra problems.

Real-World Applications

Algebra is used in various fields such as science, engineering, economics, and computer science. Some real-world applications of algebra include:

  • Science: Algebra is used to describe the laws of physics and to model the behavior of complex systems.
  • Engineering: Algebra is used to design and optimize systems, such as bridges and buildings.
  • Economics: Algebra is used to model economic systems and to make predictions about future economic trends.
  • Computer Science: Algebra is used to develop algorithms and to solve problems in computer science.

Conclusion

In conclusion, algebra is a fundamental subject that is used in various fields. Understanding the basics of algebra is essential for solving problems in mathematics and science. By following the tips and tricks outlined in this article, you can become proficient in solving algebra problems and apply your knowledge to real-world applications.