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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
xxx- dos . cinco x+ dos .5= cero
xxx menos 2.5x más 2.5 es igual a 0
xxx menos dos . cinco x más dos .5 es igual a cero
xxx-2.5x+2.5=O
Expresiones semejantes
xxx-2.5x-2.5=0
xxx+2.5x+2.5=0
Expresiones con funciones
xxx
xxx+12*6-24-9*4+72=0

xxx-2.5x+2.5=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

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

\left(x x x - \frac{5 x}{2}\right) + \frac{5}{2} = 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 = - \frac{5}{2}

v = \frac{d}{a}

v = \frac{5}{2}

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} = - \frac{5}{2}

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

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

          _________________                                /                                        _________________\
         /            ____                                 |                                       /            ____ |
        /  135   15*\/ 51                                  |                               ___    /  135   15*\/ 51  |
     3 /   --- + ---------                                 |              ___            \/ 3 *3 /   --- + --------- |
     \/     4        4                   5                 |          5*\/ 3                   \/     4        4     |
x1 = ---------------------- + ------------------------ + I*|- ------------------------ + ----------------------------|
               6                     _________________     |         _________________                6              |
                                    /            ____      |        /            ____                                |
                                   /  135   15*\/ 51       |       /  135   15*\/ 51                                 |
                              4*3 /   --- + ---------      |  4*3 /   --- + ---------                                |
                                \/     4        4          \    \/     4        4                                    /

x_{1} = \frac{5}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}} + \frac{\sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6} + i \left(- \frac{5 \sqrt{3}}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}} + \frac{\sqrt{3} \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6}\right)

          _________________                                /             _________________                           \
         /            ____                                 |            /            ____                            |
        /  135   15*\/ 51                                  |    ___    /  135   15*\/ 51                             |
     3 /   --- + ---------                                 |  \/ 3 *3 /   --- + ---------                ___         |
     \/     4        4                   5                 |        \/     4        4                5*\/ 3          |
x2 = ---------------------- + ------------------------ + I*|- ---------------------------- + ------------------------|
               6                     _________________     |               6                        _________________|
                                    /            ____      |                                       /            ____ |
                                   /  135   15*\/ 51       |                                      /  135   15*\/ 51  |
                              4*3 /   --- + ---------      |                                 4*3 /   --- + --------- |
                                \/     4        4          \                                   \/     4        4     /

x_{2} = \frac{5}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}} + \frac{\sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6} + \frac{5 \sqrt{3}}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}\right)

                                       _________________
                                      /            ____ 
                                     /  135   15*\/ 51  
                                  3 /   --- + --------- 
                  5               \/     4        4     
x3 = - ------------------------ - ----------------------
              _________________             3           
             /            ____                          
            /  135   15*\/ 51                           
       2*3 /   --- + ---------                          
         \/     4        4

x_{3} = - \frac{\sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{3} - \frac{5}{2 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}

x3 = -(15*sqrt(51)/4 + 135/4)^(1/3)/3 - 5/(2*(15*sqrt(51)/4 + 135/4)^(1/3))

Suma y producto de raíces [src]

suma

     _________________                                /                                        _________________\        _________________                                /             _________________                           \                                     _________________
    /            ____                                 |                                       /            ____ |       /            ____                                 |            /            ____                            |                                    /            ____ 
   /  135   15*\/ 51                                  |                               ___    /  135   15*\/ 51  |      /  135   15*\/ 51                                  |    ___    /  135   15*\/ 51                             |                                   /  135   15*\/ 51  
3 /   --- + ---------                                 |              ___            \/ 3 *3 /   --- + --------- |   3 /   --- + ---------                                 |  \/ 3 *3 /   --- + ---------                ___         |                                3 /   --- + --------- 
\/     4        4                   5                 |          5*\/ 3                   \/     4        4     |   \/     4        4                   5                 |        \/     4        4                5*\/ 3          |                5               \/     4        4     
---------------------- + ------------------------ + I*|- ------------------------ + ----------------------------| + ---------------------- + ------------------------ + I*|- ---------------------------- + ------------------------| + - ------------------------ - ----------------------
          6                     _________________     |         _________________                6              |             6                     _________________     |               6                        _________________|            _________________             3           
                               /            ____      |        /            ____                                |                                  /            ____      |                                       /            ____ |           /            ____                          
                              /  135   15*\/ 51       |       /  135   15*\/ 51                                 |                                 /  135   15*\/ 51       |                                      /  135   15*\/ 51  |          /  135   15*\/ 51                           
                         4*3 /   --- + ---------      |  4*3 /   --- + ---------                                |                            4*3 /   --- + ---------      |                                 4*3 /   --- + --------- |     2*3 /   --- + ---------                          
                           \/     4        4          \    \/     4        4                                    /                              \/     4        4          \                                   \/     4        4     /       \/     4        4

\left(- \frac{\sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{3} - \frac{5}{2 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}\right) + \left(\left(\frac{5}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}} + \frac{\sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6} + \frac{5 \sqrt{3}}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}\right)\right) + \left(\frac{5}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}} + \frac{\sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6} + i \left(- \frac{5 \sqrt{3}}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}} + \frac{\sqrt{3} \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6}\right)\right)\right)

  /                                        _________________\     /             _________________                           \
  |                                       /            ____ |     |            /            ____                            |
  |                               ___    /  135   15*\/ 51  |     |    ___    /  135   15*\/ 51                             |
  |              ___            \/ 3 *3 /   --- + --------- |     |  \/ 3 *3 /   --- + ---------                ___         |
  |          5*\/ 3                   \/     4        4     |     |        \/     4        4                5*\/ 3          |
I*|- ------------------------ + ----------------------------| + I*|- ---------------------------- + ------------------------|
  |         _________________                6              |     |               6                        _________________|
  |        /            ____                                |     |                                       /            ____ |
  |       /  135   15*\/ 51                                 |     |                                      /  135   15*\/ 51  |
  |  4*3 /   --- + ---------                                |     |                                 4*3 /   --- + --------- |
  \    \/     4        4                                    /     \                                   \/     4        4     /

i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6} + \frac{5 \sqrt{3}}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}\right) + i \left(- \frac{5 \sqrt{3}}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}} + \frac{\sqrt{3} \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6}\right)

producto

/     _________________                                /                                        _________________\\ /     _________________                                /             _________________                           \\ /                                  _________________\
|    /            ____                                 |                                       /            ____ || |    /            ____                                 |            /            ____                            || |                                 /            ____ |
|   /  135   15*\/ 51                                  |                               ___    /  135   15*\/ 51  || |   /  135   15*\/ 51                                  |    ___    /  135   15*\/ 51                             || |                                /  135   15*\/ 51  |
|3 /   --- + ---------                                 |              ___            \/ 3 *3 /   --- + --------- || |3 /   --- + ---------                                 |  \/ 3 *3 /   --- + ---------                ___         || |                             3 /   --- + --------- |
|\/     4        4                   5                 |          5*\/ 3                   \/     4        4     || |\/     4        4                   5                 |        \/     4        4                5*\/ 3          || |             5               \/     4        4     |
|---------------------- + ------------------------ + I*|- ------------------------ + ----------------------------||*|---------------------- + ------------------------ + I*|- ---------------------------- + ------------------------||*|- ------------------------ - ----------------------|
|          6                     _________________     |         _________________                6              || |          6                     _________________     |               6                        _________________|| |         _________________             3           |
|                               /            ____      |        /            ____                                || |                               /            ____      |                                       /            ____ || |        /            ____                          |
|                              /  135   15*\/ 51       |       /  135   15*\/ 51                                 || |                              /  135   15*\/ 51       |                                      /  135   15*\/ 51  || |       /  135   15*\/ 51                           |
|                         4*3 /   --- + ---------      |  4*3 /   --- + ---------                                || |                         4*3 /   --- + ---------      |                                 4*3 /   --- + --------- || |  2*3 /   --- + ---------                          |
\                           \/     4        4          \    \/     4        4                                    // \                           \/     4        4          \                                   \/     4        4     // \    \/     4        4                              /

\left(\frac{5}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}} + \frac{\sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6} + i \left(- \frac{5 \sqrt{3}}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}} + \frac{\sqrt{3} \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6}\right)\right) \left(\frac{5}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}} + \frac{\sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{6} + \frac{5 \sqrt{3}}{4 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}{3} - \frac{5}{2 \sqrt[3]{\frac{15 \sqrt{51}}{4} + \frac{135}{4}}}\right)

-5/2

- \frac{5}{2}

-5/2

Respuesta numérica [src]

x1 = -1.94551020654183

x2 = 0.972755103270916 - 0.582028756006808*i

x3 = 0.972755103270916 + 0.582028756006808*i

x3 = 0.972755103270916 + 0.582028756006808*i

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Expresiones con funciones

xxx-2.5x+2.5=0 la ecuación

Solución numérica:

Solución