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La ecuación:
Ecuación 6x+1=-4x
Ecuación x+y-3=0
Ecuación x^2=-3
Ecuación 9-7(x+3)=5-6x
Expresar {x} en función de y en la ecuación:
-11*x+9*y=-20
5*x-14*y=-15
-10*x+15*y=10
-9*x-6*y=12
Expresiones idénticas
(((x- uno)^ tres)/ tres)- cuatro *x= cero
(((x menos 1) al cubo ) dividir por 3) menos 4 multiplicar por x es igual a 0
(((x menos uno) en el grado tres) dividir por tres) menos cuatro multiplicar por x es igual a cero
(((x-1)3)/3)-4*x=0
x-13/3-4*x=0
(((x-1)³)/3)-4*x=0
(((x-1) en el grado 3)/3)-4*x=0
(((x-1)^3)/3)-4x=0
(((x-1)3)/3)-4x=0
x-13/3-4x=0
x-1^3/3-4x=0
(((x-1)^3)/3)-4*x=O
(((x-1)^3) dividir por 3)-4*x=0
Expresiones semejantes
(((x+1)^3)/3)-4*x=0
(((x-1)^3)/3)+4*x=0

(((x-1)^3)/3)-4*x=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

       3          
(x - 1)           
-------- - 4*x = 0
   3

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

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

            /    /  ___\\                                                /     /    /  ___\\                                                       /    /  ___\\\            /    /  ___\\
            |    |\/ 7 ||                                                |     |    |\/ 7 ||                                                       |    |\/ 7 |||            |    |\/ 7 ||
            |atan|-----||                                                |     |atan|-----||                                                       |atan|-----|||            |atan|-----||
            |    \  3  /|       /                1                 \     |     |    \  3  /|       /                1                 \     ___    |    \  3  /||     ___    |    \  3  /|
x1 = 1 - cos|-----------| + 4*re|----------------------------------| + I*|- sin|-----------| + 4*im|----------------------------------| - \/ 3 *cos|-----------|| + \/ 3 *sin|-----------|
            \     3     /       |   _______________ /          ___\|     |     \     3     /       |   _______________ /          ___\|            \     3     /|            \     3     /
                                |3 /           ___  |  1   I*\/ 3 ||     |                         |3 /           ___  |  1   I*\/ 3 ||                         |                         
                                |\/  6 + 2*I*\/ 7  *|- - - -------||     |                         |\/  6 + 2*I*\/ 7  *|- - - -------||                         |                         
                                \                   \  2      2   //     \                         \                   \  2      2   //                         /

x_{1} = - \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)} + \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 1 + i \left(- \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} - \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)}\right)

            /    /  ___\\                                                /     /    /  ___\\                                                       /    /  ___\\\            /    /  ___\\
            |    |\/ 7 ||                                                |     |    |\/ 7 ||                                                       |    |\/ 7 |||            |    |\/ 7 ||
            |atan|-----||                                                |     |atan|-----||                                                       |atan|-----|||            |atan|-----||
            |    \  3  /|       /                1                 \     |     |    \  3  /|       /                1                 \     ___    |    \  3  /||     ___    |    \  3  /|
x2 = 1 - cos|-----------| + 4*re|----------------------------------| + I*|- sin|-----------| + 4*im|----------------------------------| + \/ 3 *cos|-----------|| - \/ 3 *sin|-----------|
            \     3     /       |   _______________ /          ___\|     |     \     3     /       |   _______________ /          ___\|            \     3     /|            \     3     /
                                |3 /           ___  |  1   I*\/ 3 ||     |                         |3 /           ___  |  1   I*\/ 3 ||                         |                         
                                |\/  6 + 2*I*\/ 7  *|- - + -------||     |                         |\/  6 + 2*I*\/ 7  *|- - + -------||                         |                         
                                \                   \  2      2   //     \                         \                   \  2      2   //                         /

x_{2} = 4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)} - \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} - \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 1 + i \left(4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)} - \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)}\right)

            _______________                     
         3 /           ___            4         
x3 = 1 + \/  6 + 2*I*\/ 7   + ------------------
                                 _______________
                              3 /           ___ 
                              \/  6 + 2*I*\/ 7

x_{3} = 1 + \frac{4}{\sqrt[3]{6 + 2 \sqrt{7} i}} + \sqrt[3]{6 + 2 \sqrt{7} i}

x3 = 1 + 4/(6 + 2*sqrt(7)*i)^(1/3) + (6 + 2*sqrt(7)*i)^(1/3)

Suma y producto de raíces [src]

suma

       /    /  ___\\                                                /     /    /  ___\\                                                       /    /  ___\\\            /    /  ___\\          /    /  ___\\                                                /     /    /  ___\\                                                       /    /  ___\\\            /    /  ___\\                                              
       |    |\/ 7 ||                                                |     |    |\/ 7 ||                                                       |    |\/ 7 |||            |    |\/ 7 ||          |    |\/ 7 ||                                                |     |    |\/ 7 ||                                                       |    |\/ 7 |||            |    |\/ 7 ||                                              
       |atan|-----||                                                |     |atan|-----||                                                       |atan|-----|||            |atan|-----||          |atan|-----||                                                |     |atan|-----||                                                       |atan|-----|||            |atan|-----||          _______________                     
       |    \  3  /|       /                1                 \     |     |    \  3  /|       /                1                 \     ___    |    \  3  /||     ___    |    \  3  /|          |    \  3  /|       /                1                 \     |     |    \  3  /|       /                1                 \     ___    |    \  3  /||     ___    |    \  3  /|       3 /           ___            4         
1 - cos|-----------| + 4*re|----------------------------------| + I*|- sin|-----------| + 4*im|----------------------------------| - \/ 3 *cos|-----------|| + \/ 3 *sin|-----------| + 1 - cos|-----------| + 4*re|----------------------------------| + I*|- sin|-----------| + 4*im|----------------------------------| + \/ 3 *cos|-----------|| - \/ 3 *sin|-----------| + 1 + \/  6 + 2*I*\/ 7   + ------------------
       \     3     /       |   _______________ /          ___\|     |     \     3     /       |   _______________ /          ___\|            \     3     /|            \     3     /          \     3     /       |   _______________ /          ___\|     |     \     3     /       |   _______________ /          ___\|            \     3     /|            \     3     /                               _______________
                           |3 /           ___  |  1   I*\/ 3 ||     |                         |3 /           ___  |  1   I*\/ 3 ||                         |                                                       |3 /           ___  |  1   I*\/ 3 ||     |                         |3 /           ___  |  1   I*\/ 3 ||                         |                                                     3 /           ___ 
                           |\/  6 + 2*I*\/ 7  *|- - - -------||     |                         |\/  6 + 2*I*\/ 7  *|- - - -------||                         |                                                       |\/  6 + 2*I*\/ 7  *|- - + -------||     |                         |\/  6 + 2*I*\/ 7  *|- - + -------||                         |                                                     \/  6 + 2*I*\/ 7  
                           \                   \  2      2   //     \                         \                   \  2      2   //                         /                                                       \                   \  2      2   //     \                         \                   \  2      2   //                         /

\left(1 + \frac{4}{\sqrt[3]{6 + 2 \sqrt{7} i}} + \sqrt[3]{6 + 2 \sqrt{7} i}\right) + \left(\left(- \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)} + \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 1 + i \left(- \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} - \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)}\right)\right) + \left(4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)} - \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} - \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 1 + i \left(4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)} - \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)}\right)\right)\right)

                              /    /  ___\\                                                                                                                /     /    /  ___\\                                                       /    /  ___\\\     /     /    /  ___\\                                                       /    /  ___\\\
                              |    |\/ 7 ||                                                                                                                |     |    |\/ 7 ||                                                       |    |\/ 7 |||     |     |    |\/ 7 ||                                                       |    |\/ 7 |||
       _______________        |atan|-----||                                                                                                                |     |atan|-----||                                                       |atan|-----|||     |     |atan|-----||                                                       |atan|-----|||
    3 /           ___         |    \  3  /|           4                /                1                 \       /                1                 \     |     |    \  3  /|       /                1                 \     ___    |    \  3  /||     |     |    \  3  /|       /                1                 \     ___    |    \  3  /||
3 + \/  6 + 2*I*\/ 7   - 2*cos|-----------| + ------------------ + 4*re|----------------------------------| + 4*re|----------------------------------| + I*|- sin|-----------| + 4*im|----------------------------------| + \/ 3 *cos|-----------|| + I*|- sin|-----------| + 4*im|----------------------------------| - \/ 3 *cos|-----------||
                              \     3     /      _______________       |   _______________ /          ___\|       |   _______________ /          ___\|     |     \     3     /       |   _______________ /          ___\|            \     3     /|     |     \     3     /       |   _______________ /          ___\|            \     3     /|
                                              3 /           ___        |3 /           ___  |  1   I*\/ 3 ||       |3 /           ___  |  1   I*\/ 3 ||     |                         |3 /           ___  |  1   I*\/ 3 ||                         |     |                         |3 /           ___  |  1   I*\/ 3 ||                         |
                                              \/  6 + 2*I*\/ 7         |\/  6 + 2*I*\/ 7  *|- - + -------||       |\/  6 + 2*I*\/ 7  *|- - - -------||     |                         |\/  6 + 2*I*\/ 7  *|- - + -------||                         |     |                         |\/  6 + 2*I*\/ 7  *|- - - -------||                         |
                                                                       \                   \  2      2   //       \                   \  2      2   //     \                         \                   \  2      2   //                         /     \                         \                   \  2      2   //                         /

- 2 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)} + 4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)} + 3 + \frac{4}{\sqrt[3]{6 + 2 \sqrt{7} i}} + i \left(- \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} - \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)}\right) + i \left(4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)} - \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)}\right) + \sqrt[3]{6 + 2 \sqrt{7} i}

producto

/       /    /  ___\\                                                /     /    /  ___\\                                                       /    /  ___\\\            /    /  ___\\\ /       /    /  ___\\                                                /     /    /  ___\\                                                       /    /  ___\\\            /    /  ___\\\                                              
|       |    |\/ 7 ||                                                |     |    |\/ 7 ||                                                       |    |\/ 7 |||            |    |\/ 7 ||| |       |    |\/ 7 ||                                                |     |    |\/ 7 ||                                                       |    |\/ 7 |||            |    |\/ 7 |||                                              
|       |atan|-----||                                                |     |atan|-----||                                                       |atan|-----|||            |atan|-----||| |       |atan|-----||                                                |     |atan|-----||                                                       |atan|-----|||            |atan|-----||| /       _______________                     \
|       |    \  3  /|       /                1                 \     |     |    \  3  /|       /                1                 \     ___    |    \  3  /||     ___    |    \  3  /|| |       |    \  3  /|       /                1                 \     |     |    \  3  /|       /                1                 \     ___    |    \  3  /||     ___    |    \  3  /|| |    3 /           ___            4         |
|1 - cos|-----------| + 4*re|----------------------------------| + I*|- sin|-----------| + 4*im|----------------------------------| - \/ 3 *cos|-----------|| + \/ 3 *sin|-----------||*|1 - cos|-----------| + 4*re|----------------------------------| + I*|- sin|-----------| + 4*im|----------------------------------| + \/ 3 *cos|-----------|| - \/ 3 *sin|-----------||*|1 + \/  6 + 2*I*\/ 7   + ------------------|
|       \     3     /       |   _______________ /          ___\|     |     \     3     /       |   _______________ /          ___\|            \     3     /|            \     3     /| |       \     3     /       |   _______________ /          ___\|     |     \     3     /       |   _______________ /          ___\|            \     3     /|            \     3     /| |                            _______________|
|                           |3 /           ___  |  1   I*\/ 3 ||     |                         |3 /           ___  |  1   I*\/ 3 ||                         |                         | |                           |3 /           ___  |  1   I*\/ 3 ||     |                         |3 /           ___  |  1   I*\/ 3 ||                         |                         | |                         3 /           ___ |
|                           |\/  6 + 2*I*\/ 7  *|- - - -------||     |                         |\/  6 + 2*I*\/ 7  *|- - - -------||                         |                         | |                           |\/  6 + 2*I*\/ 7  *|- - + -------||     |                         |\/  6 + 2*I*\/ 7  *|- - + -------||                         |                         | \                         \/  6 + 2*I*\/ 7  /
\                           \                   \  2      2   //     \                         \                   \  2      2   //                         /                         / \                           \                   \  2      2   //     \                         \                   \  2      2   //                         /                         /

\left(- \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)} + \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 1 + i \left(- \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} - \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)}\right)\right) \left(4 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)} - \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} - \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + 1 + i \left(4 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + 2 \sqrt{7} i}}\right)} - \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} + \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)}\right)\right) \left(1 + \frac{4}{\sqrt[3]{6 + 2 \sqrt{7} i}} + \sqrt[3]{6 + 2 \sqrt{7} i}\right)

                                                       /          /    /  ___\\        /      /  ___\\\
                                                       |          |    |\/ 7 ||        |      |\/ 7 |||
     /       _______________ /       _______________\\ |          |atan|-----||        |2*atan|-----|||
 2/3 |    3 /           ___  |    3 /           ___ || |          |    \  3  /|        |      \  3  /||
2   *\4 + \/  6 + 2*I*\/ 7  *\1 + \/  6 + 2*I*\/ 7  //*|-3 - 4*cos|-----------| + 8*cos|-------------||
                                                       \          \     3     /        \      3      //
-------------------------------------------------------------------------------------------------------
                                                _____________                                          
                                             3 /         ___                                           
                                           2*\/  3 + I*\/ 7

\frac{2^{\frac{2}{3}} \left(4 + \left(1 + \sqrt[3]{6 + 2 \sqrt{7} i}\right) \sqrt[3]{6 + 2 \sqrt{7} i}\right) \left(- 4 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)} - 3 + 8 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{3} \right)}\right)}{2 \sqrt[3]{3 + \sqrt{7} i}}

2^(2/3)*(4 + (6 + 2*i*sqrt(7))^(1/3)*(1 + (6 + 2*i*sqrt(7))^(1/3)))*(-3 - 4*cos(atan(sqrt(7)/3)/3) + 8*cos(2*atan(sqrt(7)/3)/3))/(2*(3 + i*sqrt(7))^(1/3))

Respuesta numérica [src]

x1 = -1.76873430527628

x2 = 4.88448370193933

x3 = -0.115749396663049

x3 = -0.115749396663049

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¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

(((x-1)^3)/3)-4*x=0 la ecuación

Solución numérica:

Solución