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La ecuación:
Ecuación -x/11+x=50/11
Ecuación 12/x=3
Ecuación 6-5(4x-1)=3
Ecuación 13/(x-5)=5/(x-13)
Expresar {x} en función de y en la ecuación:
-1*x+4*y=-10
-11*x-19*y=14
8*x+6*y=20
-11*x-1*y=15
Expresiones idénticas
x^ tres +2 cero 22x+sqrt(dos mil veintiuno)=0
x al cubo más 2022x más raíz cuadrada de (2021) es igual a 0
x en el grado tres más 2 cero 22x más raíz cuadrada de (dos mil veintiuno) es igual a 0
x^3+2022x+√(2021)=0
x3+2022x+sqrt(2021)=0
x3+2022x+sqrt2021=0
x³+2022x+sqrt(2021)=0
x en el grado 3+2022x+sqrt(2021)=0
x^3+2022x+sqrt2021=0
x^3+2022x+sqrt(2021)=O
Expresiones semejantes
x^3-2022x+sqrt(2021)=0
x^3+2022x-sqrt(2021)=0
Expresiones con funciones
Raíz cuadrada sqrt
sqrt(x-a)+abs(x+a)=4
sqrt^4(17x^2-16)=x
sqrt4(4x+5-x^2)-sqrt(4x-x^2-3)=1
sqrt(log(cos(x)))=0
sqrt(x^3+x^2+1)=sqrt(2*x^2-2*x+1)

x^3+2022x+sqrt(2021)=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3              ______    
x  + 2022*x + \/ 2021  = 0

\left(x^{3} + 2022 x\right) + \sqrt{2021} = 0

Simplificar

Teorema de Cardano-Vieta

es ecuación cúbica reducida

p x^{2} + q x + v + x^{3} = 0

donde

p = \frac{b}{a}

p = 0

q = \frac{c}{a}

q = 2022

v = \frac{d}{a}

v = \sqrt{2021}

Fórmulas de Cardano-Vieta

x_{1} + x_{2} + x_{3} = - p

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q

x_{1} x_{2} x_{3} = v

x_{1} + x_{2} + x_{3} = 0

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 2022

x_{1} x_{2} x_{3} = \sqrt{2021}

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

                                                _________________________________     /                                                    _________________________________\                                                   _________________________________     /                                                      _________________________________\                                                 _________________________________
                                               /      ______        ____________      |                                                   /      ______        ____________ |                                                  /      ______        ____________      |                                                     /      ______        ____________ |                                                /      ______        ____________ 
                                              /  27*\/ 2021    27*\/ 1224730117       |                                           ___    /  27*\/ 2021    27*\/ 1224730117  |                                                 /  27*\/ 2021    27*\/ 1224730117       |                                             ___    /  27*\/ 2021    27*\/ 1224730117  |                                               /  27*\/ 2021    27*\/ 1224730117  
                                           3 /   ----------- + -----------------      |                     ___                 \/ 3 *3 /   ----------- + ----------------- |                                              3 /   ----------- + -----------------      |                       ___                 \/ 3 *3 /   ----------- + ----------------- |                                            3 /   ----------- + ----------------- 
                   1011                    \/         2                2              |              1011*\/ 3                        \/         2                2         |                      1011                    \/         2                2              |                1011*\/ 3                        \/         2                2         |                    2022                    \/         2                2         
- -------------------------------------- + -------------------------------------- + I*|-------------------------------------- + --------------------------------------------| + - -------------------------------------- + -------------------------------------- + I*|- -------------------------------------- - --------------------------------------------| + -------------------------------------- - --------------------------------------
       _________________________________                     6                        |     _________________________________                        6                      |          _________________________________                     6                        |       _________________________________                        6                      |        _________________________________                     3                   
      /      ______        ____________                                               |    /      ______        ____________                                                |         /      ______        ____________                                               |      /      ______        ____________                                                |       /      ______        ____________                                          
     /  27*\/ 2021    27*\/ 1224730117                                                |   /  27*\/ 2021    27*\/ 1224730117                                                 |        /  27*\/ 2021    27*\/ 1224730117                                                |     /  27*\/ 2021    27*\/ 1224730117                                                 |      /  27*\/ 2021    27*\/ 1224730117                                           
  3 /   ----------- + -----------------                                               |3 /   ----------- + -----------------                                                |     3 /   ----------- + -----------------                                               |  3 /   ----------- + -----------------                                                |   3 /   ----------- + -----------------                                          
  \/         2                2                                                       \\/         2                2                                                        /     \/         2                2                                                       \  \/         2                2                                                        /   \/         2                2

\left(- \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{3} + \frac{2022}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}\right) + \left(\left(- \frac{1011}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} - \frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}\right)\right) + \left(- \frac{1011}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} + i \left(\frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6}\right)\right)\right)

  /                                                      _________________________________\     /                                                    _________________________________\
  |                                                     /      ______        ____________ |     |                                                   /      ______        ____________ |
  |                                             ___    /  27*\/ 2021    27*\/ 1224730117  |     |                                           ___    /  27*\/ 2021    27*\/ 1224730117  |
  |                       ___                 \/ 3 *3 /   ----------- + ----------------- |     |                     ___                 \/ 3 *3 /   ----------- + ----------------- |
  |                1011*\/ 3                        \/         2                2         |     |              1011*\/ 3                        \/         2                2         |
I*|- -------------------------------------- - --------------------------------------------| + I*|-------------------------------------- + --------------------------------------------|
  |       _________________________________                        6                      |     |     _________________________________                        6                      |
  |      /      ______        ____________                                                |     |    /      ______        ____________                                                |
  |     /  27*\/ 2021    27*\/ 1224730117                                                 |     |   /  27*\/ 2021    27*\/ 1224730117                                                 |
  |  3 /   ----------- + -----------------                                                |     |3 /   ----------- + -----------------                                                |
  \  \/         2                2                                                        /     \\/         2                2                                                        /

i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} - \frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}\right) + i \left(\frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6}\right)

producto

/                                                _________________________________     /                                                    _________________________________\\ /                                                _________________________________     /                                                      _________________________________\\ /                                              _________________________________\
|                                               /      ______        ____________      |                                                   /      ______        ____________ || |                                               /      ______        ____________      |                                                     /      ______        ____________ || |                                             /      ______        ____________ |
|                                              /  27*\/ 2021    27*\/ 1224730117       |                                           ___    /  27*\/ 2021    27*\/ 1224730117  || |                                              /  27*\/ 2021    27*\/ 1224730117       |                                             ___    /  27*\/ 2021    27*\/ 1224730117  || |                                            /  27*\/ 2021    27*\/ 1224730117  |
|                                           3 /   ----------- + -----------------      |                     ___                 \/ 3 *3 /   ----------- + ----------------- || |                                           3 /   ----------- + -----------------      |                       ___                 \/ 3 *3 /   ----------- + ----------------- || |                                         3 /   ----------- + ----------------- |
|                   1011                    \/         2                2              |              1011*\/ 3                        \/         2                2         || |                   1011                    \/         2                2              |                1011*\/ 3                        \/         2                2         || |                 2022                    \/         2                2         |
|- -------------------------------------- + -------------------------------------- + I*|-------------------------------------- + --------------------------------------------||*|- -------------------------------------- + -------------------------------------- + I*|- -------------------------------------- - --------------------------------------------||*|-------------------------------------- - --------------------------------------|
|       _________________________________                     6                        |     _________________________________                        6                      || |       _________________________________                     6                        |       _________________________________                        6                      || |     _________________________________                     3                   |
|      /      ______        ____________                                               |    /      ______        ____________                                                || |      /      ______        ____________                                               |      /      ______        ____________                                                || |    /      ______        ____________                                          |
|     /  27*\/ 2021    27*\/ 1224730117                                                |   /  27*\/ 2021    27*\/ 1224730117                                                 || |     /  27*\/ 2021    27*\/ 1224730117                                                |     /  27*\/ 2021    27*\/ 1224730117                                                 || |   /  27*\/ 2021    27*\/ 1224730117                                           |
|  3 /   ----------- + -----------------                                               |3 /   ----------- + -----------------                                                || |  3 /   ----------- + -----------------                                               |  3 /   ----------- + -----------------                                                || |3 /   ----------- + -----------------                                          |
\  \/         2                2                                                       \\/         2                2                                                        // \  \/         2                2                                                       \  \/         2                2                                                        // \\/         2                2                                                  /

\left(- \frac{1011}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} + i \left(\frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6}\right)\right) \left(- \frac{1011}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} - \frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{3} + \frac{2022}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}\right)

 /         _______________\ 
-\2021 + \/ 2475179566457 / 
----------------------------
   ______     ____________  
 \/ 2021  + \/ 1224730117

- \frac{2021 + \sqrt{2475179566457}}{\sqrt{2021} + \sqrt{1224730117}}

-(2021 + sqrt(2475179566457))/(sqrt(2021) + sqrt(1224730117))

Respuesta rápida [src]

                                                     _________________________________     /                                                    _________________________________\
                                                    /      ______        ____________      |                                                   /      ______        ____________ |
                                                   /  27*\/ 2021    27*\/ 1224730117       |                                           ___    /  27*\/ 2021    27*\/ 1224730117  |
                                                3 /   ----------- + -----------------      |                     ___                 \/ 3 *3 /   ----------- + ----------------- |
                        1011                    \/         2                2              |              1011*\/ 3                        \/         2                2         |
x1 = - -------------------------------------- + -------------------------------------- + I*|-------------------------------------- + --------------------------------------------|
            _________________________________                     6                        |     _________________________________                        6                      |
           /      ______        ____________                                               |    /      ______        ____________                                                |
          /  27*\/ 2021    27*\/ 1224730117                                                |   /  27*\/ 2021    27*\/ 1224730117                                                 |
       3 /   ----------- + -----------------                                               |3 /   ----------- + -----------------                                                |
       \/         2                2                                                       \\/         2                2                                                        /

x_{1} = - \frac{1011}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} + i \left(\frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6}\right)

                                                     _________________________________     /                                                      _________________________________\
                                                    /      ______        ____________      |                                                     /      ______        ____________ |
                                                   /  27*\/ 2021    27*\/ 1224730117       |                                             ___    /  27*\/ 2021    27*\/ 1224730117  |
                                                3 /   ----------- + -----------------      |                       ___                 \/ 3 *3 /   ----------- + ----------------- |
                        1011                    \/         2                2              |                1011*\/ 3                        \/         2                2         |
x2 = - -------------------------------------- + -------------------------------------- + I*|- -------------------------------------- - --------------------------------------------|
            _________________________________                     6                        |       _________________________________                        6                      |
           /      ______        ____________                                               |      /      ______        ____________                                                |
          /  27*\/ 2021    27*\/ 1224730117                                                |     /  27*\/ 2021    27*\/ 1224730117                                                 |
       3 /   ----------- + -----------------                                               |  3 /   ----------- + -----------------                                                |
       \/         2                2                                                       \  \/         2                2                                                        /

x_{2} = - \frac{1011}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{6} - \frac{1011 \sqrt{3}}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}\right)

                                                   _________________________________
                                                  /      ______        ____________ 
                                                 /  27*\/ 2021    27*\/ 1224730117  
                                              3 /   ----------- + ----------------- 
                      2022                    \/         2                2         
x3 = -------------------------------------- - --------------------------------------
          _________________________________                     3                   
         /      ______        ____________                                          
        /  27*\/ 2021    27*\/ 1224730117                                           
     3 /   ----------- + -----------------                                          
     \/         2                2

x_{3} = - \frac{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}{3} + \frac{2022}{\sqrt[3]{\frac{27 \sqrt{2021}}{2} + \frac{27 \sqrt{1224730117}}{2}}}

x3 = -(27*sqrt(2021)/2 + 27*sqrt(1224730117)/2)^(1/3)/3 + 2022/(27*sqrt(2021)/2 + 27*sqrt(1224730117)/2)^(1/3)

Respuesta numérica [src]

x1 = 0.011116598070172 + 44.9666584341805*i

x2 = -0.0222331961403439

x3 = 0.011116598070172 - 44.9666584341805*i

x3 = 0.011116598070172 - 44.9666584341805*i

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¿Cómo usar?

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Expresiones semejantes

Expresiones con funciones

x^3+2022x+sqrt(2021)=0 la ecuación

Solución numérica:

Solución