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La ecuación:
Ecuación -4x+8-7=x-1
Ecuación x^4+4x^2-5=0
Ecuación x^4−17x^2+16=0
Ecuación x-2(3x+2)=16
Expresar {x} en función de y en la ecuación:
10*x+15*y=1
-8*x-4*y=-6
-13*x-14*y=-13
-6*x-2*y=7
Expresiones idénticas
x^ tres + dos mil dieciséis *x^ dos = mil ocho
x al cubo más 2016 multiplicar por x al cuadrado es igual a 1008
x en el grado tres más dos mil dieciséis multiplicar por x en el grado dos es igual a mil ocho
x3+2016*x2=1008
x³+2016*x²=1008
x en el grado 3+2016*x en el grado 2=1008
x^3+2016x^2=1008
x3+2016x2=1008
Expresiones semejantes
x^3-2016*x^2=1008
100*80=53*40+47*x

x^3+2016*x^2=1008 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3         2       
x  + 2016*x  = 1008

x^{3} + 2016 x^{2} = 1008

Simplificar

Teorema de Cardano-Vieta

es ecuación cúbica reducida

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

donde

p = \frac{b}{a}

p = 2016

q = \frac{c}{a}

q = 0

v = \frac{d}{a}

v = -1008

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} = -2016

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

x_{1} x_{2} x_{3} = -1008

Suma y producto de raíces [src]

suma

                                                                                /    /  _________\\     /                                                                           /    /  _________\\                /    /  _________\\\                /    /  _________\\                                                                                   /    /  _________\\     /                                                                           /    /  _________\\                /    /  _________\\\                /    /  _________\\                                                                                       
                                                                                |    |\/ 1204223 ||     |                                                                           |    |\/ 1204223 ||                |    |\/ 1204223 |||                |    |\/ 1204223 ||                                                                                   |    |\/ 1204223 ||     |                                                                           |    |\/ 1204223 ||                |    |\/ 1204223 |||                |    |\/ 1204223 ||                                                      _________________________________
                                                                                |atan|-----------||     |                                                                           |atan|-----------||                |atan|-----------|||                |atan|-----------||                                                                                   |atan|-----------||     |                                                                           |atan|-----------||                |atan|-----------|||                |atan|-----------||                                                   3 /                       _________ 
                /                         1                          \          |    \   602111  /|     |           /                         1                          \          |    \   602111  /|         ___    |    \   602111  /||         ___    |    \   602111  /|                   /                         1                          \          |    \   602111  /|     |           /                         1                          \          |    \   602111  /|         ___    |    \   602111  /||         ___    |    \   602111  /|                         677376                  2*\/  1024190811 + 1701*I*\/ 1204223  
-672 - 677376*re|----------------------------------------------------| + 336*cos|-----------------| + I*|- 677376*im|----------------------------------------------------| + 336*sin|-----------------| + 336*\/ 3 *cos|-----------------|| - 336*\/ 3 *sin|-----------------| + -672 - 677376*re|----------------------------------------------------| + 336*cos|-----------------| + I*|- 677376*im|----------------------------------------------------| + 336*sin|-----------------| - 336*\/ 3 *cos|-----------------|| + 336*\/ 3 *sin|-----------------| + -672 - ------------------------------------ - --------------------------------------
                |   _________________________________ /          ___\|          \        3        /     |           |   _________________________________ /          ___\|          \        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 /                       _________                                          
                |\/  1024190811 + 1701*I*\/ 1204223  *|- - - -------||                                  |           |\/  1024190811 + 1701*I*\/ 1204223  *|- - - -------||                                                                |                                                      |\/  1024190811 + 1701*I*\/ 1204223  *|- - + -------||                                  |           |\/  1024190811 + 1701*I*\/ 1204223  *|- - + -------||                                                                |                                             \/  1024190811 + 1701*I*\/ 1204223                                           
                \                                     \  2      2   //                                  \           \                                     \  2      2   //                                                                /                                                      \                                     \  2      2   //                                  \           \                                     \  2      2   //                                                                /

\left(\left(-672 - 336 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} - 677376 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)} + 336 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + i \left(- 677376 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)} + 336 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + 336 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)}\right)\right) + \left(-672 + 336 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + 336 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} - 677376 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)} + i \left(- 336 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + 336 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} - 677376 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)}\right)\right)\right) + \left(-672 - \frac{2 \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}{3} - \frac{677376}{\sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)

                                                                                                                                                                                          /    /  _________\\                                              /                                                                           /    /  _________\\                /    /  _________\\\     /                                                                           /    /  _________\\                /    /  _________\\\
                                                                                                                                                                                          |    |\/ 1204223 ||        _________________________________     |                                                                           |    |\/ 1204223 ||                |    |\/ 1204223 |||     |                                                                           |    |\/ 1204223 ||                |    |\/ 1204223 |||
                                                                                                                                                                                          |atan|-----------||     3 /                       _________      |                                                                           |atan|-----------||                |atan|-----------|||     |                                                                           |atan|-----------||                |atan|-----------|||
                       677376                           /                         1                          \            /                         1                          \          |    \   602111  /|   2*\/  1024190811 + 1701*I*\/ 1204223       |           /                         1                          \          |    \   602111  /|         ___    |    \   602111  /||     |           /                         1                          \          |    \   602111  /|         ___    |    \   602111  /||
-2016 - ------------------------------------ - 677376*re|----------------------------------------------------| - 677376*re|----------------------------------------------------| + 672*cos|-----------------| - -------------------------------------- + I*|- 677376*im|----------------------------------------------------| + 336*sin|-----------------| - 336*\/ 3 *cos|-----------------|| + I*|- 677376*im|----------------------------------------------------| + 336*sin|-----------------| + 336*\/ 3 *cos|-----------------||
           _________________________________            |   _________________________________ /          ___\|            |   _________________________________ /          ___\|          \        3        /                     3                        |           |   _________________________________ /          ___\|          \        3        /                \        3        /|     |           |   _________________________________ /          ___\|          \        3        /                \        3        /|
        3 /                       _________             |3 /                       _________  |  1   I*\/ 3 ||            |3 /                       _________  |  1   I*\/ 3 ||                                                                           |           |3 /                       _________  |  1   I*\/ 3 ||                                                                |     |           |3 /                       _________  |  1   I*\/ 3 ||                                                                |
        \/  1024190811 + 1701*I*\/ 1204223              |\/  1024190811 + 1701*I*\/ 1204223  *|- - + -------||            |\/  1024190811 + 1701*I*\/ 1204223  *|- - - -------||                                                                           |           |\/  1024190811 + 1701*I*\/ 1204223  *|- - + -------||                                                                |     |           |\/  1024190811 + 1701*I*\/ 1204223  *|- - - -------||                                                                |
                                                        \                                     \  2      2   //            \                                     \  2      2   //                                                                           \           \                                     \  2      2   //                                                                /     \           \                                     \  2      2   //                                                                /

-2016 - 677376 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)} - 677376 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)} + 672 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} - \frac{2 \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}{3} + i \left(- 336 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + 336 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} - 677376 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)}\right) + i \left(- 677376 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)} + 336 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + 336 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)}\right) - \frac{677376}{\sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}

producto

/                                                                                /    /  _________\\     /                                                                           /    /  _________\\                /    /  _________\\\                /    /  _________\\\ /                                                                                /    /  _________\\     /                                                                           /    /  _________\\                /    /  _________\\\                /    /  _________\\\                                                                                       
|                                                                                |    |\/ 1204223 ||     |                                                                           |    |\/ 1204223 ||                |    |\/ 1204223 |||                |    |\/ 1204223 ||| |                                                                                |    |\/ 1204223 ||     |                                                                           |    |\/ 1204223 ||                |    |\/ 1204223 |||                |    |\/ 1204223 ||| /                                                   _________________________________\
|                                                                                |atan|-----------||     |                                                                           |atan|-----------||                |atan|-----------|||                |atan|-----------||| |                                                                                |atan|-----------||     |                                                                           |atan|-----------||                |atan|-----------|||                |atan|-----------||| |                                                3 /                       _________ |
|                /                         1                          \          |    \   602111  /|     |           /                         1                          \          |    \   602111  /|         ___    |    \   602111  /||         ___    |    \   602111  /|| |                /                         1                          \          |    \   602111  /|     |           /                         1                          \          |    \   602111  /|         ___    |    \   602111  /||         ___    |    \   602111  /|| |                      677376                  2*\/  1024190811 + 1701*I*\/ 1204223  |
|-672 - 677376*re|----------------------------------------------------| + 336*cos|-----------------| + I*|- 677376*im|----------------------------------------------------| + 336*sin|-----------------| + 336*\/ 3 *cos|-----------------|| - 336*\/ 3 *sin|-----------------||*|-672 - 677376*re|----------------------------------------------------| + 336*cos|-----------------| + I*|- 677376*im|----------------------------------------------------| + 336*sin|-----------------| - 336*\/ 3 *cos|-----------------|| + 336*\/ 3 *sin|-----------------||*|-672 - ------------------------------------ - --------------------------------------|
|                |   _________________________________ /          ___\|          \        3        /     |           |   _________________________________ /          ___\|          \        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 /                       _________                                          |
|                |\/  1024190811 + 1701*I*\/ 1204223  *|- - - -------||                                  |           |\/  1024190811 + 1701*I*\/ 1204223  *|- - - -------||                                                                |                                   | |                |\/  1024190811 + 1701*I*\/ 1204223  *|- - + -------||                                  |           |\/  1024190811 + 1701*I*\/ 1204223  *|- - + -------||                                                                |                                   | \       \/  1024190811 + 1701*I*\/ 1204223                                           /
\                \                                     \  2      2   //                                  \           \                                     \  2      2   //                                                                /                                   / \                \                                     \  2      2   //                                  \           \                                     \  2      2   //                                                                /                                   /

\left(-672 - 336 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} - 677376 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)} + 336 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + i \left(- 677376 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)} + 336 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + 336 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)}\right)\right) \left(-672 + 336 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + 336 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} - 677376 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)} + i \left(- 336 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + 336 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} - 677376 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)}\right)\right) \left(-672 - \frac{2 \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}{3} - \frac{677376}{\sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)

                                                                                                   /              /    /  _________\\                                                                 /    /  _________\\\ /       /    /  _________\\            /    /  _________\\                                                           \
                                                                                                   |              |    |\/ 1204223 ||                                                                 |    |\/ 1204223 ||| |       |    |\/ 1204223 ||            |    |\/ 1204223 ||                                                           |
              /            _____________________________ /         _____________________________\\ |              |atan|-----------||                                                                 |atan|-----------||| |       |atan|-----------||            |atan|-----------||                                                           |
      3 _____ |         3 /                   _________  |      3 /                   _________ || |       ___    |    \   602111  /|      3 _____   /                    1                    \      |    \   602111  /|| |       |    \   602111  /|     ___    |    \   602111  /|      3 _____   /                    1                    \|
10752*\/ 147 *\112896 + \/  37932993 + 63*I*\/ 1204223  *\336 + \/  37932993 + 63*I*\/ 1204223  //*|-2 + \/ 3 *sin|-----------------| + 64*\/ 147 *re|-----------------------------------------| + cos|-----------------||*|2 - cos|-----------------| + \/ 3 *sin|-----------------| - 64*\/ 147 *re|-----------------------------------------||
                                                                                                   |              \        3        /                |                 ________________________|      \        3        /| |       \        3        /            \        3        /                |                 ________________________||
                                                                                                   |                                                 |/        ___\ 3 /              _________ |                         | |                                                                         |/        ___\ 3 /              _________ ||
                                                                                                   \                                                 \\1 - I*\/ 3 /*\/  602111 + I*\/ 1204223  /                         / \                                                                         \\1 + I*\/ 3 /*\/  602111 + I*\/ 1204223  //
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                              ________________________                                                                                                                                                           
                                                                                                                                                           3 /              _________                                                                                                                                                            
                                                                                                                                                           \/  602111 + I*\/ 1204223

\frac{10752 \sqrt[3]{147} \left(112896 + \left(336 + \sqrt[3]{37932993 + 63 \sqrt{1204223} i}\right) \sqrt[3]{37932993 + 63 \sqrt{1204223} i}\right) \left(-2 + \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + 64 \sqrt[3]{147} \operatorname{re}{\left(\frac{1}{\left(1 - \sqrt{3} i\right) \sqrt[3]{602111 + \sqrt{1204223} i}}\right)}\right) \left(- \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} - 64 \sqrt[3]{147} \operatorname{re}{\left(\frac{1}{\left(1 + \sqrt{3} i\right) \sqrt[3]{602111 + \sqrt{1204223} i}}\right)} + \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + 2\right)}{\sqrt[3]{602111 + \sqrt{1204223} i}}

10752*147^(1/3)*(112896 + (37932993 + 63*i*sqrt(1204223))^(1/3)*(336 + (37932993 + 63*i*sqrt(1204223))^(1/3)))*(-2 + sqrt(3)*sin(atan(sqrt(1204223)/602111)/3) + 64*147^(1/3)*re(1/((1 - i*sqrt(3))*(602111 + i*sqrt(1204223))^(1/3))) + cos(atan(sqrt(1204223)/602111)/3))*(2 - cos(atan(sqrt(1204223)/602111)/3) + sqrt(3)*sin(atan(sqrt(1204223)/602111)/3) - 64*147^(1/3)*re(1/((1 + i*sqrt(3))*(602111 + i*sqrt(1204223))^(1/3))))/(602111 + i*sqrt(1204223))^(1/3)

Respuesta rápida [src]

                                                                                     /    /  _________\\     /                                                                           /    /  _________\\                /    /  _________\\\                /    /  _________\\
                                                                                     |    |\/ 1204223 ||     |                                                                           |    |\/ 1204223 ||                |    |\/ 1204223 |||                |    |\/ 1204223 ||
                                                                                     |atan|-----------||     |                                                                           |atan|-----------||                |atan|-----------|||                |atan|-----------||
                     /                         1                          \          |    \   602111  /|     |           /                         1                          \          |    \   602111  /|         ___    |    \   602111  /||         ___    |    \   602111  /|
x1 = -672 - 677376*re|----------------------------------------------------| + 336*cos|-----------------| + I*|- 677376*im|----------------------------------------------------| + 336*sin|-----------------| + 336*\/ 3 *cos|-----------------|| - 336*\/ 3 *sin|-----------------|
                     |   _________________________________ /          ___\|          \        3        /     |           |   _________________________________ /          ___\|          \        3        /                \        3        /|                \        3        /
                     |3 /                       _________  |  1   I*\/ 3 ||                                  |           |3 /                       _________  |  1   I*\/ 3 ||                                                                |                                   
                     |\/  1024190811 + 1701*I*\/ 1204223  *|- - - -------||                                  |           |\/  1024190811 + 1701*I*\/ 1204223  *|- - - -------||                                                                |                                   
                     \                                     \  2      2   //                                  \           \                                     \  2      2   //                                                                /

x_{1} = -672 - 336 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} - 677376 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)} + 336 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + i \left(- 677376 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)} + 336 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + 336 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)}\right)

                                                                                     /    /  _________\\     /                                                                           /    /  _________\\                /    /  _________\\\                /    /  _________\\
                                                                                     |    |\/ 1204223 ||     |                                                                           |    |\/ 1204223 ||                |    |\/ 1204223 |||                |    |\/ 1204223 ||
                                                                                     |atan|-----------||     |                                                                           |atan|-----------||                |atan|-----------|||                |atan|-----------||
                     /                         1                          \          |    \   602111  /|     |           /                         1                          \          |    \   602111  /|         ___    |    \   602111  /||         ___    |    \   602111  /|
x2 = -672 - 677376*re|----------------------------------------------------| + 336*cos|-----------------| + I*|- 677376*im|----------------------------------------------------| + 336*sin|-----------------| - 336*\/ 3 *cos|-----------------|| + 336*\/ 3 *sin|-----------------|
                     |   _________________________________ /          ___\|          \        3        /     |           |   _________________________________ /          ___\|          \        3        /                \        3        /|                \        3        /
                     |3 /                       _________  |  1   I*\/ 3 ||                                  |           |3 /                       _________  |  1   I*\/ 3 ||                                                                |                                   
                     |\/  1024190811 + 1701*I*\/ 1204223  *|- - + -------||                                  |           |\/  1024190811 + 1701*I*\/ 1204223  *|- - + -------||                                                                |                                   
                     \                                     \  2      2   //                                  \           \                                     \  2      2   //                                                                /

x_{2} = -672 + 336 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + 336 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} - 677376 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)} + i \left(- 336 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} + 336 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{1204223}}{602111} \right)}}{3} \right)} - 677376 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}\right)}\right)

                                                        _________________________________
                                                     3 /                       _________ 
                           677376                  2*\/  1024190811 + 1701*I*\/ 1204223  
x3 = -672 - ------------------------------------ - --------------------------------------
               _________________________________                     3                   
            3 /                       _________                                          
            \/  1024190811 + 1701*I*\/ 1204223

x_{3} = -672 - \frac{2 \sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}{3} - \frac{677376}{\sqrt[3]{1024190811 + 1701 \sqrt{1204223} i}}

x3 = -672 - 2*(1024190811 + 1701*sqrt(1204223)*i)^(1/3)/3 - 677376/(1024190811 + 1701*sqrt(1204223)*i)^(1/3)

Respuesta numérica [src]

x1 = -2015.99975198407

x2 = 0.706982827588875

x3 = -0.707230843522915

x3 = -0.707230843522915

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Expresiones idénticas

Expresiones semejantes

x^3+2016*x^2=1008 la ecuación

Solución numérica:

Solución