Asignaturas

Matemáticas

Álgebra

Inecuaciones y sistemas

How to Solve Polynomial and Exponential Equations

Name: Knowunity
Brand: Knowunity

Ver

How to Solve Polynomial and Exponential Equations

Paula Soler

@paulasoler_aisb

157 Seguidores

Seguir

A comprehensive guide to solving various types of equations and systems of equations, focusing on advanced mathematical techniques and methods.

The guide covers sistemas de ecuaciones lineales métodos de solución and various equation types including polynomial, radical, logarithmic, and exponential equations
Detailed explanations of solving techniques for equations up to degree 20 (ecuaciones polinómicas de grado 20 cómo resolver)
Special emphasis on ecuaciones exponenciales cambio de variable técnic and transformation methods
Includes classification of equation systems and their solutions
Features practical examples and step-by-step solution methods

21/5/2023

514

ecuaciones y
sistemas
Ecuación polinómica de grado 20
Ec. Polinómica de gradė> 2
Qx² + bx²³ + ²x²fdx + f = 0
Ec bicuadradas
Qx4 + 5x²+C =0
C

Ver

Irrational and Logarithmic Equations

This section focuses on equations involving radicals and logarithms, presenting key solving strategies.

Definition: Irrational equations contain variables under root signs or radicals.

The solving process involves:

Isolating the radical term
Squaring both sides
Verification of solutions

Highlight: Solution verification is crucial in radical equations to eliminate extraneous solutions.

Example: For logarithmic equations like log x² - log(x+4) = log 2, combine logarithm properties and solve algebraically.

Ver

Exponential Equations

This chapter details three main types of exponential equation solving methods.

Definition: Exponential equations are equations where variables appear in exponents.

Example: 2^(x+3) - 2^(x+4) - 16 = 0 can be solved using substitution method.

Three main types covered:

Same base expressions
Variable substitution method
Logarithmic solution method

Highlight: The change of variable technique (ecuaciones exponenciales cambio de variable técnic) is particularly useful for complex exponential equations.

Ver

Linear Equation Systems

This section explores methods for solving systems of linear equations.

Definition: A system of linear equations consists of two or more linear equations that must be solved simultaneously.

Four main solution methods:

Substitution
Elimination
Equalization
Graphical method

Example: For the system {3x+6y=7, -x-3y=-5}, use substitution to find x=3, y=-2.

Ver

Classification of Equation Systems

This section categorizes different types of equation systems and their solutions.

Definition: Systems can be classified as compatible (determined or undetermined) or incompatible based on their solution sets.

Three main classifications:

Systems with unique solutions (Compatible Determined)
Systems with infinite solutions (Compatible Undetermined)
Systems with no solutions (Incompatible)

Highlight: Understanding system classification is crucial for choosing appropriate solution methods.

Ver

Non-Linear Equation Systems

This final section covers advanced systems including exponential and logarithmic equations.

Definition: Non-linear systems contain equations of degree higher than one or involve transcendental functions.

Example: A system combining exponential equations like {5^x + 2^y = 33, 5^x - 2^y = 1} requires specialized solving techniques.

Highlight: Variable substitution is often key in solving complex non-linear systems.

Ver

Polynomial and Rational Equations

This section introduces fundamental concepts of polynomial and rational equations, including methods for solving equations of varying degrees.

Definition: Polynomial equations are equations containing variables raised to non-negative integer powers.

Example: ax² + bx + c = 0 is a quadratic equation where a, b, and c are constants and a ≠ 0.

Highlight: For equations of degree 20 or higher, specialized techniques and computer assistance may be required.

The page covers three main types of equations:

Complete polynomial equations
Incomplete polynomial equations
Rational equations with algebraic fractions

Vocabulary: Rational equations are those containing algebraic fractions where variables may appear in denominators.

Contenido similar

489

4° ESO

Inecuaciones

Ejercicios y teoría de: inecuaciones de grado 1, inecuaciones de grado 2, inecuaciones de grado mayor q 2, sistemas de inecuaciones, inecuaciones de fracciones algebraicas, inecuaciones con 2 incógnitas y sistemas de inecuaciones con 2 incógnitas.

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Knowunity es la app educativa nº 1 en cinco países europeos

Knowunity fue un artículo destacado por Apple y ha ocupado sistemáticamente los primeros puestos en las listas de la tienda de aplicaciones dentro de la categoría de educación en Alemania, Italia, Polonia, Suiza y Reino Unido. Regístrate hoy en Knowunity y ayuda a millones de estudiantes de todo el mundo.

Descargar en

Google Play

Descargar en

App Store

Knowunity es la app educativa nº 1 en cinco países europeos

4.9+

valoración media de la app

15 M

A los alumnos les encanta Knowunity

#1

en las listas de aplicaciones educativas de 12 países

950 K+

alumnos han subido contenidos escolares

¿Aún no estás convencido? Mira lo que dicen tus compañeros...

Usuario de iOS

Me encanta esta app [...] ¡¡¡Recomiendo Knowunity a todo el mundo!!! Pasé de un 2 a un 9 con él :D

Javi, usuario de iOS

La app es muy fácil de usar y está muy bien diseñada. Hasta ahora he encontrado todo lo que estaba buscando y he podido aprender mucho de las presentaciones.

Mari, usuario de iOS

Me encanta esta app ❤️, de hecho la uso cada vez que estudio.

Asignaturas

Matemáticas

Álgebra

Inecuaciones y sistemas

How to Solve Polynomial and Exponential Equations

Paula Soler

@paulasoler_aisb

157 Seguidores

Seguir

A comprehensive guide to solving various types of equations and systems of equations, focusing on advanced mathematical techniques and methods.

The guide covers sistemas de ecuaciones lineales métodos de solución and various equation types including polynomial, radical, logarithmic, and exponential equations
Detailed explanations of solving techniques for equations up to degree 20 (ecuaciones polinómicas de grado 20 cómo resolver)
Special emphasis on ecuaciones exponenciales cambio de variable técnic and transformation methods
Includes classification of equation systems and their solutions
Features practical examples and step-by-step solution methods

21/5/2023

514

4° ESO

Matemáticas

Inscríbete para ver los apuntes. ¡Es gratis!

Acceso a todos los documentos

Mejora tus notas

Únete a millones de estudiantes

Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.

Irrational and Logarithmic Equations

This section focuses on equations involving radicals and logarithms, presenting key solving strategies.

Definition: Irrational equations contain variables under root signs or radicals.

The solving process involves:

Isolating the radical term
Squaring both sides
Verification of solutions

Highlight: Solution verification is crucial in radical equations to eliminate extraneous solutions.

Example: For logarithmic equations like log x² - log(x+4) = log 2, combine logarithm properties and solve algebraically.

Inscríbete para ver los apuntes. ¡Es gratis!

Acceso a todos los documentos

Mejora tus notas

Únete a millones de estudiantes

Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.

Exponential Equations

This chapter details three main types of exponential equation solving methods.

Definition: Exponential equations are equations where variables appear in exponents.

Example: 2^(x+3) - 2^(x+4) - 16 = 0 can be solved using substitution method.

Three main types covered:

Same base expressions
Variable substitution method
Logarithmic solution method

Highlight: The change of variable technique (ecuaciones exponenciales cambio de variable técnic) is particularly useful for complex exponential equations.

Inscríbete para ver los apuntes. ¡Es gratis!

Acceso a todos los documentos

Mejora tus notas

Únete a millones de estudiantes

Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.

Linear Equation Systems

This section explores methods for solving systems of linear equations.

Definition: A system of linear equations consists of two or more linear equations that must be solved simultaneously.

Four main solution methods:

Substitution
Elimination
Equalization
Graphical method

Example: For the system {3x+6y=7, -x-3y=-5}, use substitution to find x=3, y=-2.

Inscríbete para ver los apuntes. ¡Es gratis!

Acceso a todos los documentos

Mejora tus notas

Únete a millones de estudiantes

Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.

Classification of Equation Systems

This section categorizes different types of equation systems and their solutions.

Definition: Systems can be classified as compatible (determined or undetermined) or incompatible based on their solution sets.

Three main classifications:

Systems with unique solutions (Compatible Determined)
Systems with infinite solutions (Compatible Undetermined)
Systems with no solutions (Incompatible)

Highlight: Understanding system classification is crucial for choosing appropriate solution methods.

Inscríbete para ver los apuntes. ¡Es gratis!

Acceso a todos los documentos

Mejora tus notas

Únete a millones de estudiantes

Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.

Non-Linear Equation Systems

This final section covers advanced systems including exponential and logarithmic equations.

Definition: Non-linear systems contain equations of degree higher than one or involve transcendental functions.

Example: A system combining exponential equations like {5^x + 2^y = 33, 5^x - 2^y = 1} requires specialized solving techniques.

Highlight: Variable substitution is often key in solving complex non-linear systems.

Inscríbete para ver los apuntes. ¡Es gratis!

Acceso a todos los documentos

Mejora tus notas

Únete a millones de estudiantes

Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.

Polynomial and Rational Equations

This section introduces fundamental concepts of polynomial and rational equations, including methods for solving equations of varying degrees.

Definition: Polynomial equations are equations containing variables raised to non-negative integer powers.

Example: ax² + bx + c = 0 is a quadratic equation where a, b, and c are constants and a ≠ 0.

Highlight: For equations of degree 20 or higher, specialized techniques and computer assistance may be required.

The page covers three main types of equations:

Complete polynomial equations
Incomplete polynomial equations
Rational equations with algebraic fractions

Vocabulary: Rational equations are those containing algebraic fractions where variables may appear in denominators.

Contenido similar

Matemáticas - Inecuaciones

489

¿No encuentras lo que buscas? Explora otros temas.

Knowunity es la app educativa nº 1 en cinco países europeos

Knowunity fue un artículo destacado por Apple y ha ocupado sistemáticamente los primeros puestos en las listas de la tienda de aplicaciones dentro de la categoría de educación en Alemania, Italia, Polonia, Suiza y Reino Unido. Regístrate hoy en Knowunity y ayuda a millones de estudiantes de todo el mundo.

Descargar en

Google Play

Descargar en

App Store

4.9+

valoración media de la app

15 M

A los alumnos les encanta Knowunity

#1

en las listas de aplicaciones educativas de 12 países

950 K+

alumnos han subido contenidos escolares

¿Aún no estás convencido? Mira lo que dicen tus compañeros...

Usuario de iOS

Me encanta esta app [...] ¡¡¡Recomiendo Knowunity a todo el mundo!!! Pasé de un 2 a un 9 con él :D

Javi, usuario de iOS

La app es muy fácil de usar y está muy bien diseñada. Hasta ahora he encontrado todo lo que estaba buscando y he podido aprender mucho de las presentaciones.

Mari, usuario de iOS