Basic Algebra: Showing E = .5(k/a) Without The Conjugate

In summary, Basic Algebra is a branch of mathematics that deals with operations and relationships involving variables, constants, and equations. E = .5(k/a) is a mathematical expression representing the relationship between three variables: E, k, and a, where E is half of k divided by a. The conjugate is used to simplify this expression and make it easier to solve. However, it is also important to understand how to show E = .5(k/a) without using the conjugate, as it demonstrates a deeper understanding of algebraic concepts and allows for more flexibility in solving equations. It also lays a strong foundation for more complex algebraic operations and problem-solving in the future.
  • #1
Nusc
760
2
Can someone explain to me why E = .5(k/a)(e^2 - 1)/(1 - e^2) = .5(k/a)

The conjugate won't work, how do I show this?
 
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  • #2
Nusc said:
Can someone explain to me why E = .5(k/a)(e^2 - 1)/(1 - e^2) = .5(k/a)
The conjugate won't work, how do I show this?

You can factor -1 out of the denominator and then cancel (e^2-1), but that leaves you with E = .5(k/a)(e^2 - 1)/(1 - e^2) = -.5(k/a)

GM
 
  • #3
Actually that was what I meant 0.5(k/a), thanks
 

FAQ: Basic Algebra: Showing E = .5(k/a) Without The Conjugate

1. What is "Basic Algebra"?

Basic Algebra is the branch of mathematics that deals with operations and relationships involving variables, constants, and equations.

2. What does "E = .5(k/a)" mean?

E = .5(k/a) is a mathematical expression that represents the relationship between three variables: E, k, and a. It indicates that E is equal to half of k divided by a.

3. What is the significance of the "conjugate" in this equation?

The conjugate refers to the operation of multiplying the numerator and denominator of a fraction by the same expression, but with opposite signs. In this case, it is used to simplify the expression E = .5(k/a) to make it easier to solve.

4. How do you show E = .5(k/a) without using the conjugate?

To show E = .5(k/a) without using the conjugate, you can use the properties of fractions to simplify the expression. For example, you can multiply both sides by 2 to get rid of the decimal and then divide both sides by k to isolate E.

5. Why is it important to understand how to show E = .5(k/a) without using the conjugate?

Understanding how to show E = .5(k/a) without using the conjugate is important because it demonstrates a deeper understanding of algebraic concepts and allows for more flexibility in solving equations. It also lays a strong foundation for more complex algebraic operations and problem-solving in the future.

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