Theory of Equations of First Degree

 

This theory about Equations is the continue of the previous post “How to solve an equation”

 

Theory of Biquadrate Equations.

 

To solve a biquadrate equation follow these steps:

 

1. If there are parentheses and/or brackets, they are resolved with the necessary operation.

2. If there are denominators, it is estimated the m.c.m. and we reduce all fractions to this common denominator.

3. Denominators are removed once reduced all terms to m.c.m.

4. Each term is simplifies the most possible.

5. All terms are left on a member and it is equals to zero.

6. The unknown “x²” is replaced by “t” thereby obtaining a quadratic equation.

7. The quadratic equation is solved.

8. It is performed again replacing, “t” by “x²”, and the square root is performed to obtains the values of “x”.

 

Example:

 

Theory of Equation of degree greater than two.

 

To solve a degree equation greater than two, not being biquadratic, we apply the Ruffini method as it is explained in Polynomials theory.

In case of grade 3 or higher and, having no independent term, we have to extract common factor “x” and resolve it as it is seen in the example.

 

Example:

 

Theory of notables identities.

 

Squared binomial:

Examples:

Sum by difference:

Example:

 

 

 

 

You can download the App BioProfe READER to practice this theory with self-corrected exercises.