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Ecuación x=(x+1)/2
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Ecuación x^2-14*x+33=0
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Ecuación 5-x^2=0
- Expresar {x} en función de y en la ecuación:
- 12*x+1*y=15
- -17*x-12*y=-9
- 18*x+17*y=-14
- 14*x-10*y=-4
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Expresiones idénticas
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- menos x al cubo menos 3 multiplicar por x al cuadrado más 14 multiplicar por x más 28 es igual a 0
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- -x3-3*x2+14*x+28=0
- -x³-3*x²+14*x+28=0
- -x en el grado 3-3*x en el grado 2+14*x+28=0
- -x^3-3x^2+14x+28=0
- -x3-3x2+14x+28=0
- -x^3-3*x^2+14*x+28=O
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Expresiones semejantes
- -x^3-3*x^2+14*x-28=0
- -x^3+3*x^2+14*x+28=0
- -x^3-3*x^2-14*x+28=0
- x^3-3*x^2+14*x+28=0
-x^3-3*x^2+14*x+28=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 - x - 3*x + 14*x + 28 = 0
$$\left(14 x + \left(- x^{3} - 3 x^{2}\right)\right) + 28 = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(14 x + \left(- x^{3} - 3 x^{2}\right)\right) + 28 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + 3 x^{2} - 14 x - 28 = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 3$$
$$q = \frac{c}{a}$$
$$q = -14$$
$$v = \frac{d}{a}$$
$$v = -28$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -3$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -14$$
$$x_{1} x_{2} x_{3} = -28$$
$$\left(14 x + \left(- x^{3} - 3 x^{2}\right)\right) + 28 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + 3 x^{2} - 14 x - 28 = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 3$$
$$q = \frac{c}{a}$$
$$q = -14$$
$$v = \frac{d}{a}$$
$$v = -28$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -3$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -14$$
$$x_{1} x_{2} x_{3} = -28$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
17*re|--------------------------------------| |17*im|--------------------------------------| / / _______\\ / / _______\\| / / _______\\ / / _______\\
| _________________ | | | _________________ | | |\/ 11823 || | |\/ 11823 ||| | |\/ 11823 || | |\/ 11823 ||
| / _______ / ___\| | | / _______ / ___\| |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------||
| / I*\/ 11823 | 1 I*\/ 3 || | | / I*\/ 11823 | 1 I*\/ 3 || ____ | \ 54 /| ____ | \ 54 /|| ____ | \ 54 /| ____ | \ 54 /|
|3 / 6 + ----------- *|- - - -------|| | |3 / 6 + ----------- *|- - - -------|| \/ 17 *cos|---------------| \/ 51 *sin|---------------|| \/ 17 *sin|---------------| \/ 51 *cos|---------------|
\\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = -1 + --------------------------------------------- + I*|--------------------------------------------- - --------------------------- - ---------------------------| + --------------------------- - ---------------------------
3 \ 3 2 6 / 2 6
$$x_{1} = - \frac{\sqrt{51} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} - 1 + \frac{17 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3} + \frac{\sqrt{17} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{17} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2} - \frac{\sqrt{51} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} + \frac{17 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3}\right)$$
/ 1 \ / / 1 \ \
17*re|--------------------------------------| |17*im|--------------------------------------| / / _______\\ / / _______\\| / / _______\\ / / _______\\
| _________________ | | | _________________ | | |\/ 11823 || | |\/ 11823 ||| | |\/ 11823 || | |\/ 11823 ||
| / _______ / ___\| | | / _______ / ___\| |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------||
| / I*\/ 11823 | 1 I*\/ 3 || | | / I*\/ 11823 | 1 I*\/ 3 || ____ | \ 54 /| ____ | \ 54 /|| ____ | \ 54 /| ____ | \ 54 /|
|3 / 6 + ----------- *|- - + -------|| | |3 / 6 + ----------- *|- - + -------|| \/ 17 *cos|---------------| \/ 51 *sin|---------------|| \/ 17 *sin|---------------| \/ 51 *cos|---------------|
\\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = -1 + --------------------------------------------- + I*|--------------------------------------------- + --------------------------- - ---------------------------| - --------------------------- - ---------------------------
3 \ 3 2 6 / 2 6
$$x_{2} = \frac{17 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3} - \frac{\sqrt{51} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} - 1 - \frac{\sqrt{17} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2} + i \left(\frac{17 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3} - \frac{\sqrt{51} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} + \frac{\sqrt{17} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2}\right)$$
_________________
/ _______
/ I*\/ 11823 17
x3 = -1 + 3 / 6 + ----------- + ------------------------
\/ 9 _________________
/ _______
/ I*\/ 11823
3*3 / 6 + -----------
\/ 9
$$x_{3} = -1 + \frac{17}{3 \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}} + \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}$$
x3 = -1 + 17/(3*(6 + sqrt(11823)*i/9)^(1/3)) + (6 + sqrt(11823)*i/9)^(1/3)
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
17*re|--------------------------------------| |17*im|--------------------------------------| / / _______\\ / / _______\\| / / _______\\ / / _______\\ 17*re|--------------------------------------| |17*im|--------------------------------------| / / _______\\ / / _______\\| / / _______\\ / / _______\\
| _________________ | | | _________________ | | |\/ 11823 || | |\/ 11823 ||| | |\/ 11823 || | |\/ 11823 || | _________________ | | | _________________ | | |\/ 11823 || | |\/ 11823 ||| | |\/ 11823 || | |\/ 11823 ||
| / _______ / ___\| | | / _______ / ___\| |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------|| | / _______ / ___\| | | / _______ / ___\| |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------||
| / I*\/ 11823 | 1 I*\/ 3 || | | / I*\/ 11823 | 1 I*\/ 3 || ____ | \ 54 /| ____ | \ 54 /|| ____ | \ 54 /| ____ | \ 54 /| | / I*\/ 11823 | 1 I*\/ 3 || | | / I*\/ 11823 | 1 I*\/ 3 || ____ | \ 54 /| ____ | \ 54 /|| ____ | \ 54 /| ____ | \ 54 /| _________________
|3 / 6 + ----------- *|- - - -------|| | |3 / 6 + ----------- *|- - - -------|| \/ 17 *cos|---------------| \/ 51 *sin|---------------|| \/ 17 *sin|---------------| \/ 51 *cos|---------------| |3 / 6 + ----------- *|- - + -------|| | |3 / 6 + ----------- *|- - + -------|| \/ 17 *cos|---------------| \/ 51 *sin|---------------|| \/ 17 *sin|---------------| \/ 51 *cos|---------------| / _______
\\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 / \\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 / / I*\/ 11823 17
-1 + --------------------------------------------- + I*|--------------------------------------------- - --------------------------- - ---------------------------| + --------------------------- - --------------------------- + -1 + --------------------------------------------- + I*|--------------------------------------------- + --------------------------- - ---------------------------| - --------------------------- - --------------------------- + -1 + 3 / 6 + ----------- + ------------------------
3 \ 3 2 6 / 2 6 3 \ 3 2 6 / 2 6 \/ 9 _________________
/ _______
/ I*\/ 11823
3*3 / 6 + -----------
\/ 9
$$\left(-1 + \frac{17}{3 \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}} + \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}\right) + \left(\left(- \frac{\sqrt{51} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} - 1 + \frac{17 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3} + \frac{\sqrt{17} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{17} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2} - \frac{\sqrt{51} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} + \frac{17 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3}\right)\right) + \left(\frac{17 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3} - \frac{\sqrt{51} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} - 1 - \frac{\sqrt{17} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2} + i \left(\frac{17 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3} - \frac{\sqrt{51} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} + \frac{\sqrt{17} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2}\right)\right)\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
17*re|--------------------------------------| 17*re|--------------------------------------| |17*im|--------------------------------------| / / _______\\ / / _______\\| |17*im|--------------------------------------| / / _______\\ / / _______\\| / / _______\\
| _________________ | | _________________ | | | _________________ | | |\/ 11823 || | |\/ 11823 ||| | | _________________ | | |\/ 11823 || | |\/ 11823 ||| | |\/ 11823 ||
| / _______ / ___\| | / _______ / ___\| | | / _______ / ___\| |atan|---------|| |atan|---------||| | | / _______ / ___\| |atan|---------|| |atan|---------||| |atan|---------||
_________________ | / I*\/ 11823 | 1 I*\/ 3 || | / I*\/ 11823 | 1 I*\/ 3 || | | / I*\/ 11823 | 1 I*\/ 3 || ____ | \ 54 /| ____ | \ 54 /|| | | / I*\/ 11823 | 1 I*\/ 3 || ____ | \ 54 /| ____ | \ 54 /|| ____ | \ 54 /|
/ _______ |3 / 6 + ----------- *|- - + -------|| |3 / 6 + ----------- *|- - - -------|| | |3 / 6 + ----------- *|- - + -------|| \/ 17 *cos|---------------| \/ 51 *sin|---------------|| | |3 / 6 + ----------- *|- - - -------|| \/ 17 *cos|---------------| \/ 51 *sin|---------------|| \/ 51 *cos|---------------|
/ I*\/ 11823 17 \\/ 9 \ 2 2 // \\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 /
-3 + 3 / 6 + ----------- + ------------------------ + --------------------------------------------- + --------------------------------------------- + I*|--------------------------------------------- + --------------------------- - ---------------------------| + I*|--------------------------------------------- - --------------------------- - ---------------------------| - ---------------------------
\/ 9 _________________ 3 3 \ 3 2 6 / \ 3 2 6 / 3
/ _______
/ I*\/ 11823
3*3 / 6 + -----------
\/ 9
$$-3 - \frac{\sqrt{51} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{3} + \frac{17 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3} + \frac{17 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3} + \frac{17}{3 \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}} + i \left(\frac{17 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3} - \frac{\sqrt{51} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} + \frac{\sqrt{17} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2}\right) + i \left(- \frac{\sqrt{17} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2} - \frac{\sqrt{51} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} + \frac{17 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3}\right) + \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 17*re|--------------------------------------| |17*im|--------------------------------------| / / _______\\ / / _______\\| / / _______\\ / / _______\\| | 17*re|--------------------------------------| |17*im|--------------------------------------| / / _______\\ / / _______\\| / / _______\\ / / _______\\|
| | _________________ | | | _________________ | | |\/ 11823 || | |\/ 11823 ||| | |\/ 11823 || | |\/ 11823 ||| | | _________________ | | | _________________ | | |\/ 11823 || | |\/ 11823 ||| | |\/ 11823 || | |\/ 11823 |||
| | / _______ / ___\| | | / _______ / ___\| |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------||| | | / _______ / ___\| | | / _______ / ___\| |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------|||
| | / I*\/ 11823 | 1 I*\/ 3 || | | / I*\/ 11823 | 1 I*\/ 3 || ____ | \ 54 /| ____ | \ 54 /|| ____ | \ 54 /| ____ | \ 54 /|| | | / I*\/ 11823 | 1 I*\/ 3 || | | / I*\/ 11823 | 1 I*\/ 3 || ____ | \ 54 /| ____ | \ 54 /|| ____ | \ 54 /| ____ | \ 54 /|| / _________________ \
| |3 / 6 + ----------- *|- - - -------|| | |3 / 6 + ----------- *|- - - -------|| \/ 17 *cos|---------------| \/ 51 *sin|---------------|| \/ 17 *sin|---------------| \/ 51 *cos|---------------|| | |3 / 6 + ----------- *|- - + -------|| | |3 / 6 + ----------- *|- - + -------|| \/ 17 *cos|---------------| \/ 51 *sin|---------------|| \/ 17 *sin|---------------| \/ 51 *cos|---------------|| | / _______ |
| \\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /| | \\/ 9 \ 2 2 // | \\/ 9 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /| | / I*\/ 11823 17 |
|-1 + --------------------------------------------- + I*|--------------------------------------------- - --------------------------- - ---------------------------| + --------------------------- - ---------------------------|*|-1 + --------------------------------------------- + I*|--------------------------------------------- + --------------------------- - ---------------------------| - --------------------------- - ---------------------------|*|-1 + 3 / 6 + ----------- + ------------------------|
\ 3 \ 3 2 6 / 2 6 / \ 3 \ 3 2 6 / 2 6 / | \/ 9 _________________|
| / _______ |
| / I*\/ 11823 |
| 3*3 / 6 + ----------- |
\ \/ 9 /
$$\left(- \frac{\sqrt{51} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} - 1 + \frac{17 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3} + \frac{\sqrt{17} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{17} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2} - \frac{\sqrt{51} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} + \frac{17 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3}\right)\right) \left(\frac{17 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3} - \frac{\sqrt{51} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} - 1 - \frac{\sqrt{17} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2} + i \left(\frac{17 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}}\right)}}{3} - \frac{\sqrt{51} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{6} + \frac{\sqrt{17} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}}{2}\right)\right) \left(-1 + \frac{17}{3 \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}} + \sqrt[3]{6 + \frac{\sqrt{11823} i}{9}}\right)$$
=
/ / / _______\\ / / _______\\\
| | |\/ 11823 || | |\/ 11823 |||
/ __________________ / _____________________\\ | |2*atan|---------|| |atan|---------|||
| 2/3 3 / _______ | 3 / _______ || | | \ 54 /| ____ | \ 54 /||
\17*3 + \/ 54 + I*\/ 11823 *\-3 + \/ 162 + 3*I*\/ 11823 //*|-168 + 408*cos|-----------------| + 24*\/ 51 *cos|---------------||
\ \ 3 / \ 3 //
--------------------------------------------------------------------------------------------------------------------------------------
__________________
3 / _______
108*\/ 54 + I*\/ 11823
$$\frac{\left(17 \cdot 3^{\frac{2}{3}} + \left(-3 + \sqrt[3]{162 + 3 \sqrt{11823} i}\right) \sqrt[3]{54 + \sqrt{11823} i}\right) \left(-168 + 24 \sqrt{51} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)} + 408 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{\sqrt{11823}}{54} \right)}}{3} \right)}\right)}{108 \sqrt[3]{54 + \sqrt{11823} i}}$$
(17*3^(2/3) + (54 + i*sqrt(11823))^(1/3)*(-3 + (162 + 3*i*sqrt(11823))^(1/3)))*(-168 + 408*cos(2*atan(sqrt(11823)/54)/3) + 24*sqrt(51)*cos(atan(sqrt(11823)/54)/3))/(108*(54 + i*sqrt(11823))^(1/3))
Respuesta numérica
[src]
x1 = 3.43885143209577
x2 = -1.72863784621664
x3 = -4.71021358587913
x3 = -4.71021358587913