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La ecuación:
Ecuación 3*x^2-x+2=0
Ecuación x^2=-74
Ecuación z^2+z+1=0
Ecuación 90+x-4*10=60
Expresar {x} en función de y en la ecuación:
5*x+19*y=-3
9*x+14*y=-10
-4*x-8*y=-20
-12*x-10*y=-16
Expresiones idénticas
5 cero x^ tres -1185x^ dos +4614x+ mil novecientos cincuenta y tres =0
50x al cubo menos 1185x al cuadrado más 4614x más 1953 es igual a 0
5 cero x en el grado tres menos 1185x en el grado dos más 4614x más mil novecientos cincuenta y tres es igual a 0
50x3-1185x2+4614x+1953=0
50x³-1185x²+4614x+1953=0
50x en el grado 3-1185x en el grado 2+4614x+1953=0
50x^3-1185x^2+4614x+1953=O
Expresiones semejantes
50x^3+1185x^2+4614x+1953=0
50x^3-1185x^2+4614x-1953=0
50x^3-1185x^2-4614x+1953=0

50x^3-1185x^2+4614x+1953=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

    3         2                    
50*x  - 1185*x  + 4614*x + 1953 = 0

\left(4614 x + \left(50 x^{3} - 1185 x^{2}\right)\right) + 1953 = 0

Simplificar

Teorema de Cardano-Vieta

reescribamos la ecuación

\left(4614 x + \left(50 x^{3} - 1185 x^{2}\right)\right) + 1953 = 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{237 x^{2}}{10} + \frac{2307 x}{25} + \frac{1953}{50} = 0

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

donde

p = \frac{b}{a}

p = - \frac{237}{10}

q = \frac{c}{a}

q = \frac{2307}{25}

v = \frac{d}{a}

v = \frac{1953}{50}

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{237}{10}

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = \frac{2307}{25}

x_{1} x_{2} x_{3} = \frac{1953}{50}

Respuesta rápida [src]

                /                       1                        \     /      /                       1                        \                                                                                \                                                                                
          633*re|------------------------------------------------|     |633*im|------------------------------------------------|                 /    /    ____________\\               /    /    ____________\\|               /    /    ____________\\                 /    /    ____________\\
                |                     ___________________________|     |      |                     ___________________________|                 |    |2*\/ 4955715779 ||               |    |2*\/ 4955715779 |||               |    |2*\/ 4955715779 ||                 |    |2*\/ 4955715779 ||
                |/          ___\     /              ____________ |     |      |/          ___\     /              ____________ |                 |atan|----------------||               |atan|----------------|||               |atan|----------------||                 |atan|----------------||
                ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |     |      ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |       ______    |    \     109003     /|     ______    |    \     109003     /||     ______    |    \     109003     /|       ______    |    \     109003     /|
                ||- - - -------|*3 /   ------ + ---------------- |     |      ||- - - -------|*3 /   ------ + ---------------- |   3*\/ 1055 *cos|----------------------|   \/ 3165 *sin|----------------------||   \/ 3165 *cos|----------------------|   3*\/ 1055 *sin|----------------------|
     79         \\  2      2   / \/     1000          500        /     |      \\  2      2   / \/     1000          500        /                 \          3           /               \          3           /|               \          3           /                 \          3           /
x1 = -- + -------------------------------------------------------- + I*|-------------------------------------------------------- - -------------------------------------- - ------------------------------------| - ------------------------------------ + --------------------------------------
     10                              20                                \                           20                                                20                                      20                 /                    20                                      20

x_{1} = - \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} + \frac{3 \sqrt{1055} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{79}{10} + i \left(- \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20}\right)

                /                       1                        \     /      /                       1                        \                                                                                \                                                                                
          633*re|------------------------------------------------|     |633*im|------------------------------------------------|               /    /    ____________\\                 /    /    ____________\\|                 /    /    ____________\\               /    /    ____________\\
                |                     ___________________________|     |      |                     ___________________________|               |    |2*\/ 4955715779 ||                 |    |2*\/ 4955715779 |||                 |    |2*\/ 4955715779 ||               |    |2*\/ 4955715779 ||
                |/          ___\     /              ____________ |     |      |/          ___\     /              ____________ |               |atan|----------------||                 |atan|----------------|||                 |atan|----------------||               |atan|----------------||
                ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |     |      ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |     ______    |    \     109003     /|       ______    |    \     109003     /||       ______    |    \     109003     /|     ______    |    \     109003     /|
                ||- - + -------|*3 /   ------ + ---------------- |     |      ||- - + -------|*3 /   ------ + ---------------- |   \/ 3165 *sin|----------------------|   3*\/ 1055 *cos|----------------------||   3*\/ 1055 *sin|----------------------|   \/ 3165 *cos|----------------------|
     79         \\  2      2   / \/     1000          500        /     |      \\  2      2   / \/     1000          500        /               \          3           /                 \          3           /|                 \          3           /               \          3           /
x2 = -- + -------------------------------------------------------- + I*|-------------------------------------------------------- - ------------------------------------ + --------------------------------------| - -------------------------------------- - ------------------------------------
     10                              20                                \                           20                                               20                                      20                  /                     20                                      20

x_{2} = \frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{3 \sqrt{1055} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{79}{10} + i \left(\frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20}\right)

               ___________________________                                      
              /              ____________                                       
     79      /  109003   I*\/ 4955715779                     633                
x3 = -- + 3 /   ------ + ----------------  + -----------------------------------
     10   \/     1000          500                   ___________________________
                                                    /              ____________ 
                                                   /  109003   I*\/ 4955715779  
                                             20*3 /   ------ + ---------------- 
                                                \/     1000          500

x_{3} = \frac{79}{10} + \frac{633}{20 \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}} + \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}

x3 = 79/10 + 633/(20*(109003/1000 + sqrt(4955715779)*i/500)^(1/3)) + (109003/1000 + sqrt(4955715779)*i/500)^(1/3)

Suma y producto de raíces [src]

suma

           /                       1                        \     /      /                       1                        \                                                                                \                                                                                              /                       1                        \     /      /                       1                        \                                                                                \                                                                                                                                                              
     633*re|------------------------------------------------|     |633*im|------------------------------------------------|                 /    /    ____________\\               /    /    ____________\\|               /    /    ____________\\                 /    /    ____________\\        633*re|------------------------------------------------|     |633*im|------------------------------------------------|               /    /    ____________\\                 /    /    ____________\\|                 /    /    ____________\\               /    /    ____________\\                                                                              
           |                     ___________________________|     |      |                     ___________________________|                 |    |2*\/ 4955715779 ||               |    |2*\/ 4955715779 |||               |    |2*\/ 4955715779 ||                 |    |2*\/ 4955715779 ||              |                     ___________________________|     |      |                     ___________________________|               |    |2*\/ 4955715779 ||                 |    |2*\/ 4955715779 |||                 |    |2*\/ 4955715779 ||               |    |2*\/ 4955715779 ||                                                                              
           |/          ___\     /              ____________ |     |      |/          ___\     /              ____________ |                 |atan|----------------||               |atan|----------------|||               |atan|----------------||                 |atan|----------------||              |/          ___\     /              ____________ |     |      |/          ___\     /              ____________ |               |atan|----------------||                 |atan|----------------|||                 |atan|----------------||               |atan|----------------||                                                                              
           ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |     |      ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |       ______    |    \     109003     /|     ______    |    \     109003     /||     ______    |    \     109003     /|       ______    |    \     109003     /|              ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |     |      ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |     ______    |    \     109003     /|       ______    |    \     109003     /||       ______    |    \     109003     /|     ______    |    \     109003     /|             ___________________________                                      
           ||- - - -------|*3 /   ------ + ---------------- |     |      ||- - - -------|*3 /   ------ + ---------------- |   3*\/ 1055 *cos|----------------------|   \/ 3165 *sin|----------------------||   \/ 3165 *cos|----------------------|   3*\/ 1055 *sin|----------------------|              ||- - + -------|*3 /   ------ + ---------------- |     |      ||- - + -------|*3 /   ------ + ---------------- |   \/ 3165 *sin|----------------------|   3*\/ 1055 *cos|----------------------||   3*\/ 1055 *sin|----------------------|   \/ 3165 *cos|----------------------|            /              ____________                                       
79         \\  2      2   / \/     1000          500        /     |      \\  2      2   / \/     1000          500        /                 \          3           /               \          3           /|               \          3           /                 \          3           /   79         \\  2      2   / \/     1000          500        /     |      \\  2      2   / \/     1000          500        /               \          3           /                 \          3           /|                 \          3           /               \          3           /   79      /  109003   I*\/ 4955715779                     633                
-- + -------------------------------------------------------- + I*|-------------------------------------------------------- - -------------------------------------- - ------------------------------------| - ------------------------------------ + -------------------------------------- + -- + -------------------------------------------------------- + I*|-------------------------------------------------------- - ------------------------------------ + --------------------------------------| - -------------------------------------- - ------------------------------------ + -- + 3 /   ------ + ----------------  + -----------------------------------
10                              20                                \                           20                                                20                                      20                 /                    20                                      20                     10                              20                                \                           20                                               20                                      20                  /                     20                                      20                    10   \/     1000          500                   ___________________________
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             /              ____________ 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            /  109003   I*\/ 4955715779  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      20*3 /   ------ + ---------------- 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         \/     1000          500

\left(\frac{79}{10} + \frac{633}{20 \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}} + \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}\right) + \left(\left(- \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} + \frac{3 \sqrt{1055} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{79}{10} + i \left(- \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20}\right)\right) + \left(\frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{3 \sqrt{1055} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{79}{10} + i \left(\frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20}\right)\right)\right)

                                                                                     /                       1                        \         /                       1                        \     /      /                       1                        \                                                                                \     /      /                       1                        \                                                                                \                                       
                                                                               633*re|------------------------------------------------|   633*re|------------------------------------------------|     |633*im|------------------------------------------------|               /    /    ____________\\                 /    /    ____________\\|     |633*im|------------------------------------------------|                 /    /    ____________\\               /    /    ____________\\|               /    /    ____________\\
                                                                                     |                     ___________________________|         |                     ___________________________|     |      |                     ___________________________|               |    |2*\/ 4955715779 ||                 |    |2*\/ 4955715779 |||     |      |                     ___________________________|                 |    |2*\/ 4955715779 ||               |    |2*\/ 4955715779 |||               |    |2*\/ 4955715779 ||
                                                                                     |/          ___\     /              ____________ |         |/          ___\     /              ____________ |     |      |/          ___\     /              ____________ |               |atan|----------------||                 |atan|----------------|||     |      |/          ___\     /              ____________ |                 |atan|----------------||               |atan|----------------|||               |atan|----------------||
           ___________________________                                               ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |         ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |     |      ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |     ______    |    \     109003     /|       ______    |    \     109003     /||     |      ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |       ______    |    \     109003     /|     ______    |    \     109003     /||     ______    |    \     109003     /|
          /              ____________                                                ||- - + -------|*3 /   ------ + ---------------- |         ||- - - -------|*3 /   ------ + ---------------- |     |      ||- - + -------|*3 /   ------ + ---------------- |   \/ 3165 *sin|----------------------|   3*\/ 1055 *cos|----------------------||     |      ||- - - -------|*3 /   ------ + ---------------- |   3*\/ 1055 *cos|----------------------|   \/ 3165 *sin|----------------------||   \/ 3165 *cos|----------------------|
237      /  109003   I*\/ 4955715779                     633                         \\  2      2   / \/     1000          500        /         \\  2      2   / \/     1000          500        /     |      \\  2      2   / \/     1000          500        /               \          3           /                 \          3           /|     |      \\  2      2   / \/     1000          500        /                 \          3           /               \          3           /|               \          3           /
--- + 3 /   ------ + ----------------  + ----------------------------------- + -------------------------------------------------------- + -------------------------------------------------------- + I*|-------------------------------------------------------- - ------------------------------------ + --------------------------------------| + I*|-------------------------------------------------------- - -------------------------------------- - ------------------------------------| - ------------------------------------
 10   \/     1000          500                   ___________________________                              20                                                         20                                \                           20                                               20                                      20                  /     \                           20                                                20                                      20                 /                    10                 
                                                /              ____________                                                                                                                                                                                                                                                                                                                                                                                                                                                            
                                               /  109003   I*\/ 4955715779                                                                                                                                                                                                                                                                                                                                                                                                                                                             
                                         20*3 /   ------ + ----------------                                                                                                                                                                                                                                                                                                                                                                                                                                                            
                                            \/     1000          500

- \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{10} + \frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} + \frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} + \frac{237}{10} + \frac{633}{20 \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}} + i \left(- \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20}\right) + i \left(\frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20}\right) + \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}

producto

/           /                       1                        \     /      /                       1                        \                                                                                \                                                                                \ /           /                       1                        \     /      /                       1                        \                                                                                \                                                                                \                                                                              
|     633*re|------------------------------------------------|     |633*im|------------------------------------------------|                 /    /    ____________\\               /    /    ____________\\|               /    /    ____________\\                 /    /    ____________\\| |     633*re|------------------------------------------------|     |633*im|------------------------------------------------|               /    /    ____________\\                 /    /    ____________\\|                 /    /    ____________\\               /    /    ____________\\|                                                                              
|           |                     ___________________________|     |      |                     ___________________________|                 |    |2*\/ 4955715779 ||               |    |2*\/ 4955715779 |||               |    |2*\/ 4955715779 ||                 |    |2*\/ 4955715779 ||| |           |                     ___________________________|     |      |                     ___________________________|               |    |2*\/ 4955715779 ||                 |    |2*\/ 4955715779 |||                 |    |2*\/ 4955715779 ||               |    |2*\/ 4955715779 |||                                                                              
|           |/          ___\     /              ____________ |     |      |/          ___\     /              ____________ |                 |atan|----------------||               |atan|----------------|||               |atan|----------------||                 |atan|----------------||| |           |/          ___\     /              ____________ |     |      |/          ___\     /              ____________ |               |atan|----------------||                 |atan|----------------|||                 |atan|----------------||               |atan|----------------|||                                                                              
|           ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |     |      ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |       ______    |    \     109003     /|     ______    |    \     109003     /||     ______    |    \     109003     /|       ______    |    \     109003     /|| |           ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |     |      ||  1   I*\/ 3 |    /  109003   I*\/ 4955715779  |     ______    |    \     109003     /|       ______    |    \     109003     /||       ______    |    \     109003     /|     ______    |    \     109003     /|| /          ___________________________                                      \
|           ||- - - -------|*3 /   ------ + ---------------- |     |      ||- - - -------|*3 /   ------ + ---------------- |   3*\/ 1055 *cos|----------------------|   \/ 3165 *sin|----------------------||   \/ 3165 *cos|----------------------|   3*\/ 1055 *sin|----------------------|| |           ||- - + -------|*3 /   ------ + ---------------- |     |      ||- - + -------|*3 /   ------ + ---------------- |   \/ 3165 *sin|----------------------|   3*\/ 1055 *cos|----------------------||   3*\/ 1055 *sin|----------------------|   \/ 3165 *cos|----------------------|| |         /              ____________                                       |
|79         \\  2      2   / \/     1000          500        /     |      \\  2      2   / \/     1000          500        /                 \          3           /               \          3           /|               \          3           /                 \          3           /| |79         \\  2      2   / \/     1000          500        /     |      \\  2      2   / \/     1000          500        /               \          3           /                 \          3           /|                 \          3           /               \          3           /| |79      /  109003   I*\/ 4955715779                     633                |
|-- + -------------------------------------------------------- + I*|-------------------------------------------------------- - -------------------------------------- - ------------------------------------| - ------------------------------------ + --------------------------------------|*|-- + -------------------------------------------------------- + I*|-------------------------------------------------------- - ------------------------------------ + --------------------------------------| - -------------------------------------- - ------------------------------------|*|-- + 3 /   ------ + ----------------  + -----------------------------------|
\10                              20                                \                           20                                                20                                      20                 /                    20                                      20                  / \10                              20                                \                           20                                               20                                      20                  /                     20                                      20                 / |10   \/     1000          500                   ___________________________|
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |                                               /              ____________ |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |                                              /  109003   I*\/ 4955715779  |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |                                        20*3 /   ------ + ---------------- |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              \                                           \/     1000          500        /

\left(- \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} + \frac{3 \sqrt{1055} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{79}{10} + i \left(- \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20}\right)\right) \left(\frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{3 \sqrt{1055} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{79}{10} + i \left(\frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20}\right)\right) \left(\frac{79}{10} + \frac{633}{20 \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}} + \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}\right)

                                                                                  /                 /      /    ____________\\                   /    /    ____________\\\
                                                                                  |                 |      |2*\/ 4955715779 ||                   |    |2*\/ 4955715779 |||
/          _____________________________ /        _____________________________\\ |                 |2*atan|----------------||                   |atan|----------------|||
|       3 /                ____________  |     3 /                ____________ || |                 |      \     109003     /|         ______    |    \     109003     /||
\3165 + \/  109003 + 2*I*\/ 4955715779  *\79 + \/  109003 + 2*I*\/ 4955715779  //*|12304 + 25320*cos|------------------------| - 632*\/ 3165 *cos|----------------------||
                                                                                  \                 \           3            /                   \          3           //
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                          _____________________________                                                                   
                                                                       3 /                ____________                                                                    
                                                                  4000*\/  109003 + 2*I*\/ 4955715779

\frac{\left(3165 + \left(79 + \sqrt[3]{109003 + 2 \sqrt{4955715779} i}\right) \sqrt[3]{109003 + 2 \sqrt{4955715779} i}\right) \left(- 632 \sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)} + 12304 + 25320 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}\right)}{4000 \sqrt[3]{109003 + 2 \sqrt{4955715779} i}}

(3165 + (109003 + 2*i*sqrt(4955715779))^(1/3)*(79 + (109003 + 2*i*sqrt(4955715779))^(1/3)))*(12304 + 25320*cos(2*atan(2*sqrt(4955715779)/109003)/3) - 632*sqrt(3165)*cos(atan(2*sqrt(4955715779)/109003)/3))/(4000*(109003 + 2*i*sqrt(4955715779))^(1/3))

Respuesta numérica [src]

x1 = 18.6357593234578

x2 = -0.384659360573435

x3 = 5.44890003711563

x3 = 5.44890003711563

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