Solving a•b=(a+b)^2 with no Identity for Real Numbers

Thread starter Zashmar
Start date Apr 18, 2013
Tags

Groups

In summary, the equation "Solving a•b=(a+b)^2 with no Identity for Real Numbers" involves finding the values of two variables (a and b) that satisfy the equation. The phrase "no Identity for Real Numbers" means that the values of a and b can be any real numbers. Solving this equation is important for understanding the relationship between variables and manipulating mathematical expressions. The possible solutions for this equation are infinite, but some values may make it easier to solve. To solve this equation, you can expand the expression, rearrange, factor, and use the Zero Product Property to find the solutions for a and b.

Apr 18, 2013

Zashmar

Show that a•b=(a+b)^2 has no identity for real numbers
Hi this is a new topic please help
Thanks

Physics news on Phys.org

Apr 18, 2013

HallsofIvy

Science Advisor

Homework Helper

An "identity" for an operation would be a member of the group, I, such at a•I= I•a= a. So you just need to show there is no number, I, such that (a+ I)^2= a for every a.

1. What is the equation "Solving a•b=(a+b)^2 with no Identity for Real Numbers"?

The equation "Solving a•b=(a+b)^2 with no Identity for Real Numbers" is a mathematical expression that involves two variables (a and b) and requires finding the values of a and b that satisfy the equation.

2. What does "no Identity for Real Numbers" mean in this context?

In this context, "no Identity for Real Numbers" means that there is no specific value or identity assigned to the variables a and b. This means that the values of a and b can be any real numbers, rather than being limited to a specific number or set of numbers.

3. What is the importance of solving this equation?

Solving this equation is important in mathematics as it helps to understand the relationship between variables and how they affect each other. It also allows for the manipulation and simplification of mathematical expressions to solve more complex problems.

4. What are the possible solutions for this equation?

The possible solutions for this equation can be any real numbers that satisfy the equation. This means that there are infinite solutions, as there are infinite real numbers. However, some values may make the equation easier to solve or more applicable to a specific problem.

5. How can I solve this equation step-by-step?

To solve this equation, you can follow these steps:
1. Expand the expression (a+b)^2 to get a^2 + 2ab + b^2
2. Rearrange the equation to get a^2 + 2ab - a•b + b^2 = 0
3. Factor out a common term of a and b to get a(a+2b) - b(a+2b) = 0
4. Simplify to get (a-b)(a+2b) = 0
5. Use the Zero Product Property to find the possible values of a and b that make the equation true. This means that either (a-b)=0 or (a+2b)=0
6. Solve for a and b to find the solutions to the equation.