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La ecuación:
Ecuación 4^x-3*2^x+2=0
Ecuación (x-2)/(x-7)=5/8
Ecuación 4/(x-4)=-5
Ecuación (x-6)^2=-24*x
Expresar {x} en función de y en la ecuación:
20*x+5*y=-3
-11*x-14*y=-3
20*x+18*y=-9
-2*x+2*y=4
Expresiones idénticas
(5x^ tres + dos x^ dos +3x- uno)/(2)
(5x al cubo más 2x al cuadrado más 3x menos 1) dividir por (2)
(5x en el grado tres más dos x en el grado dos más 3x menos uno) dividir por (2)
(5x3+2x2+3x-1)/(2)
5x3+2x2+3x-1/2
(5x³+2x²+3x-1)/(2)
(5x en el grado 3+2x en el grado 2+3x-1)/(2)
5x^3+2x^2+3x-1/2
(5x^3+2x^2+3x-1) dividir por (2)
Expresiones semejantes
(5x^3-2x^2+3x-1)/(2)
(5x^3+2x^2+3x+1)/(2)
(5x^3+2x^2-3x-1)/(2)

(5x^3+2x^2+3x-1)/(2) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

   3      2              
5*x  + 2*x  + 3*x - 1    
--------------------- = 0
          2

\frac{\left(3 x + \left(5 x^{3} + 2 x^{2}\right)\right) - 1}{2} = 0

Simplificar

Teorema de Cardano-Vieta

reescribamos la ecuación

\frac{\left(3 x + \left(5 x^{3} + 2 x^{2}\right)\right) - 1}{2} = 0

a x^{3} + b x^{2} + c x + d = 0

como ecuación cúbica reducida

x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0

x^{3} + \frac{2 x^{2}}{5} + \frac{3 x}{5} - \frac{1}{5} = 0

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

donde

p = \frac{b}{a}

p = \frac{2}{5}

q = \frac{c}{a}

q = \frac{3}{5}

v = \frac{d}{a}

v = - \frac{1}{5}

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} = - \frac{2}{5}

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = \frac{3}{5}

x_{1} x_{2} x_{3} = - \frac{1}{5}

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

            _________________                                  /                                          _________________\               _________________                                  /           _________________                             \                                                             
           /          ______                                   |                                         /          ______ |              /          ______                                   |          /          ______                              |                                                             
          /  929    \/ 5061                                    |                                 ___    /  929    \/ 5061  |             /  929    \/ 5061                                    |  ___    /  929    \/ 5061                               |               _________________                             
       3 /   ---- + --------                                   |                ___            \/ 3 *3 /   ---- + -------- |          3 /   ---- + --------                                   |\/ 3 *3 /   ---- + --------                  ___         |              /          ______                              
  2    \/    6750     450                   41                 |           41*\/ 3                   \/    6750     450    |     2    \/    6750     450                   41                 |      \/    6750     450                41*\/ 3          |     2       /  929    \/ 5061                 41            
- -- - ---------------------- + -------------------------- + I*|- -------------------------- - ----------------------------| + - -- - ---------------------- + -------------------------- + I*|---------------------------- + --------------------------| + - -- + 3 /   ---- + --------  - --------------------------
  15             2                       _________________     |           _________________                2              |     15             2                       _________________     |             2                          _________________|     15   \/    6750     450                _________________
                                        /          ______      |          /          ______                                |                                           /          ______      |                                       /          ______ |                                           /          ______ 
                                       /  929    \/ 5061       |         /  929    \/ 5061                                 |                                          /  929    \/ 5061       |                                      /  929    \/ 5061  |                                          /  929    \/ 5061  
                                450*3 /   ---- + --------      |  450*3 /   ---- + --------                                |                                   450*3 /   ---- + --------      |                               450*3 /   ---- + -------- |                                   225*3 /   ---- + -------- 
                                    \/    6750     450         \      \/    6750     450                                   /                                       \/    6750     450         \                                   \/    6750     450    /                                       \/    6750     450

\left(- \frac{41}{225 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}} - \frac{2}{15} + \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2} - \frac{2}{15} + \frac{41}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2} - \frac{41 \sqrt{3}}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2} - \frac{2}{15} + \frac{41}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}} + i \left(\frac{41 \sqrt{3}}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}} + \frac{\sqrt{3} \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2}\right)\right)\right)

        /           _________________                             \     /                                          _________________\
        |          /          ______                              |     |                                         /          ______ |
        |  ___    /  929    \/ 5061                               |     |                                 ___    /  929    \/ 5061  |
        |\/ 3 *3 /   ---- + --------                  ___         |     |                ___            \/ 3 *3 /   ---- + -------- |
  2     |      \/    6750     450                41*\/ 3          |     |           41*\/ 3                   \/    6750     450    |
- - + I*|---------------------------- + --------------------------| + I*|- -------------------------- - ----------------------------|
  5     |             2                          _________________|     |           _________________                2              |
        |                                       /          ______ |     |          /          ______                                |
        |                                      /  929    \/ 5061  |     |         /  929    \/ 5061                                 |
        |                               450*3 /   ---- + -------- |     |  450*3 /   ---- + --------                                |
        \                                   \/    6750     450    /     \      \/    6750     450                                   /

- \frac{2}{5} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2} - \frac{41 \sqrt{3}}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}\right) + i \left(\frac{41 \sqrt{3}}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}} + \frac{\sqrt{3} \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2}\right)

producto

/            _________________                                  /                                          _________________\\ /            _________________                                  /           _________________                             \\                                                             
|           /          ______                                   |                                         /          ______ || |           /          ______                                   |          /          ______                              ||                                                             
|          /  929    \/ 5061                                    |                                 ___    /  929    \/ 5061  || |          /  929    \/ 5061                                    |  ___    /  929    \/ 5061                               || /            _________________                             \
|       3 /   ---- + --------                                   |                ___            \/ 3 *3 /   ---- + -------- || |       3 /   ---- + --------                                   |\/ 3 *3 /   ---- + --------                  ___         || |           /          ______                              |
|  2    \/    6750     450                   41                 |           41*\/ 3                   \/    6750     450    || |  2    \/    6750     450                   41                 |      \/    6750     450                41*\/ 3          || |  2       /  929    \/ 5061                 41            |
|- -- - ---------------------- + -------------------------- + I*|- -------------------------- - ----------------------------||*|- -- - ---------------------- + -------------------------- + I*|---------------------------- + --------------------------||*|- -- + 3 /   ---- + --------  - --------------------------|
|  15             2                       _________________     |           _________________                2              || |  15             2                       _________________     |             2                          _________________|| |  15   \/    6750     450                _________________|
|                                        /          ______      |          /          ______                                || |                                        /          ______      |                                       /          ______ || |                                        /          ______ |
|                                       /  929    \/ 5061       |         /  929    \/ 5061                                 || |                                       /  929    \/ 5061       |                                      /  929    \/ 5061  || |                                       /  929    \/ 5061  |
|                                450*3 /   ---- + --------      |  450*3 /   ---- + --------                                || |                                450*3 /   ---- + --------      |                               450*3 /   ---- + -------- || |                                225*3 /   ---- + -------- |
\                                    \/    6750     450         \      \/    6750     450                                   // \                                    \/    6750     450         \                                   \/    6750     450    // \                                    \/    6750     450    /

\left(- \frac{\sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2} - \frac{2}{15} + \frac{41}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}} + i \left(\frac{41 \sqrt{3}}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}} + \frac{\sqrt{3} \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2} - \frac{2}{15} + \frac{41}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2} - \frac{41 \sqrt{3}}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}\right)\right) \left(- \frac{41}{225 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}} - \frac{2}{15} + \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}\right)

1/5

\frac{1}{5}

1/5

Respuesta rápida [src]

                 _________________                                  /                                          _________________\
                /          ______                                   |                                         /          ______ |
               /  929    \/ 5061                                    |                                 ___    /  929    \/ 5061  |
            3 /   ---- + --------                                   |                ___            \/ 3 *3 /   ---- + -------- |
       2    \/    6750     450                   41                 |           41*\/ 3                   \/    6750     450    |
x1 = - -- - ---------------------- + -------------------------- + I*|- -------------------------- - ----------------------------|
       15             2                       _________________     |           _________________                2              |
                                             /          ______      |          /          ______                                |
                                            /  929    \/ 5061       |         /  929    \/ 5061                                 |
                                     450*3 /   ---- + --------      |  450*3 /   ---- + --------                                |
                                         \/    6750     450         \      \/    6750     450                                   /

x_{1} = - \frac{\sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2} - \frac{2}{15} + \frac{41}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2} - \frac{41 \sqrt{3}}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}\right)

                 _________________                                  /           _________________                             \
                /          ______                                   |          /          ______                              |
               /  929    \/ 5061                                    |  ___    /  929    \/ 5061                               |
            3 /   ---- + --------                                   |\/ 3 *3 /   ---- + --------                  ___         |
       2    \/    6750     450                   41                 |      \/    6750     450                41*\/ 3          |
x2 = - -- - ---------------------- + -------------------------- + I*|---------------------------- + --------------------------|
       15             2                       _________________     |             2                          _________________|
                                             /          ______      |                                       /          ______ |
                                            /  929    \/ 5061       |                                      /  929    \/ 5061  |
                                     450*3 /   ---- + --------      |                               450*3 /   ---- + -------- |
                                         \/    6750     450         \                                   \/    6750     450    /

x_{2} = - \frac{\sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2} - \frac{2}{15} + \frac{41}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}} + i \left(\frac{41 \sqrt{3}}{450 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}} + \frac{\sqrt{3} \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}}{2}\right)

                 _________________                             
                /          ______                              
       2       /  929    \/ 5061                 41            
x3 = - -- + 3 /   ---- + --------  - --------------------------
       15   \/    6750     450                _________________
                                             /          ______ 
                                            /  929    \/ 5061  
                                     225*3 /   ---- + -------- 
                                         \/    6750     450

x_{3} = - \frac{41}{225 \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}} - \frac{2}{15} + \sqrt[3]{\frac{929}{6750} + \frac{\sqrt{5061}}{450}}

x3 = -41/(225*(929/6750 + sqrt(5061)/450)^(1/3)) - 2/15 + (929/6750 + sqrt(5061)/450)^(1/3)

Respuesta numérica [src]

x1 = -0.329695073882822 - 0.813843023021972*i

x2 = 0.259390147765645

x3 = -0.329695073882822 + 0.813843023021972*i

x3 = -0.329695073882822 + 0.813843023021972*i

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Expresiones idénticas

Expresiones semejantes

(5x^3+2x^2+3x-1)/(2) la ecuación

Solución numérica:

Solución