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-2*x^3-4*x^2+37*x-26=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 - 2*x - 4*x + 37*x - 26 = 0
$$\left(37 x + \left(- 2 x^{3} - 4 x^{2}\right)\right) - 26 = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(37 x + \left(- 2 x^{3} - 4 x^{2}\right)\right) - 26 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + 2 x^{2} - \frac{37 x}{2} + 13 = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = - \frac{37}{2}$$
$$v = \frac{d}{a}$$
$$v = 13$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -2$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{37}{2}$$
$$x_{1} x_{2} x_{3} = 13$$
$$\left(37 x + \left(- 2 x^{3} - 4 x^{2}\right)\right) - 26 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + 2 x^{2} - \frac{37 x}{2} + 13 = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = - \frac{37}{2}$$
$$v = \frac{d}{a}$$
$$v = 13$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -2$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{37}{2}$$
$$x_{1} x_{2} x_{3} = 13$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
119*re|------------------------------------------| | 119*im|------------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| _____________________ | | | _____________________ | | |3*\/ 3198 || | |3*\/ 3198 ||| | |3*\/ 3198 || | |3*\/ 3198 ||
| / ______ / ___\| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
| / 21*I*\/ 3198 | 1 I*\/ 3 || | | / 21*I*\/ 3198 | 1 I*\/ 3 || _____ | \ 200 /| _____ | \ 200 /|| _____ | \ 200 /| _____ | \ 200 /|
|3 / 350 + ------------- *|- - - -------|| | |3 / 350 + ------------- *|- - - -------|| \/ 238 *sin|----------------| \/ 714 *cos|----------------|| \/ 714 *sin|----------------| \/ 238 *cos|----------------|
2 \\/ 4 \ 2 2 // | \\/ 4 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = - - - -------------------------------------------------- + I*|- -------------------------------------------------- + ----------------------------- + -----------------------------| - ----------------------------- + -----------------------------
3 6 \ 6 12 12 / 12 12
$$x_{1} = - \frac{2}{3} - \frac{\sqrt{714} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} - \frac{119 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6} + \frac{\sqrt{238} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + i \left(- \frac{119 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6} + \frac{\sqrt{238} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + \frac{\sqrt{714} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12}\right)$$
/ 1 \ / / 1 \ \
119*re|------------------------------------------| | 119*im|------------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| _____________________ | | | _____________________ | | |3*\/ 3198 || | |3*\/ 3198 ||| | |3*\/ 3198 || | |3*\/ 3198 ||
| / ______ / ___\| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
| / 21*I*\/ 3198 | 1 I*\/ 3 || | | / 21*I*\/ 3198 | 1 I*\/ 3 || _____ | \ 200 /| _____ | \ 200 /|| _____ | \ 200 /| _____ | \ 200 /|
|3 / 350 + ------------- *|- - + -------|| | |3 / 350 + ------------- *|- - + -------|| \/ 714 *cos|----------------| \/ 238 *sin|----------------|| \/ 238 *cos|----------------| \/ 714 *sin|----------------|
2 \\/ 4 \ 2 2 // | \\/ 4 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = - - - -------------------------------------------------- + I*|- -------------------------------------------------- - ----------------------------- + -----------------------------| + ----------------------------- + -----------------------------
3 6 \ 6 12 12 / 12 12
$$x_{2} = - \frac{2}{3} + \frac{\sqrt{714} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + \frac{\sqrt{238} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} - \frac{119 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6} + i \left(- \frac{\sqrt{714} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + \frac{\sqrt{238} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} - \frac{119 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6}\right)$$
_____________________
/ ______
/ 21*I*\/ 3198
3 / 350 + -------------
2 119 \/ 4
x3 = - - - ---------------------------- - --------------------------
3 _____________________ 3
/ ______
/ 21*I*\/ 3198
6*3 / 350 + -------------
\/ 4
$$x_{3} = - \frac{2}{3} - \frac{\sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}{3} - \frac{119}{6 \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}$$
x3 = -2/3 - (350 + 21*sqrt(3198)*i/4)^(1/3)/3 - 119/(6*(350 + 21*sqrt(3198)*i/4)^(1/3))
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
119*re|------------------------------------------| | 119*im|------------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\ 119*re|------------------------------------------| | 119*im|------------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| _____________________ | | | _____________________ | | |3*\/ 3198 || | |3*\/ 3198 ||| | |3*\/ 3198 || | |3*\/ 3198 || | _____________________ | | | _____________________ | | |3*\/ 3198 || | |3*\/ 3198 ||| | |3*\/ 3198 || | |3*\/ 3198 || _____________________
| / ______ / ___\| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| | / ______ / ___\| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| / ______
| / 21*I*\/ 3198 | 1 I*\/ 3 || | | / 21*I*\/ 3198 | 1 I*\/ 3 || _____ | \ 200 /| _____ | \ 200 /|| _____ | \ 200 /| _____ | \ 200 /| | / 21*I*\/ 3198 | 1 I*\/ 3 || | | / 21*I*\/ 3198 | 1 I*\/ 3 || _____ | \ 200 /| _____ | \ 200 /|| _____ | \ 200 /| _____ | \ 200 /| / 21*I*\/ 3198
|3 / 350 + ------------- *|- - - -------|| | |3 / 350 + ------------- *|- - - -------|| \/ 238 *sin|----------------| \/ 714 *cos|----------------|| \/ 714 *sin|----------------| \/ 238 *cos|----------------| |3 / 350 + ------------- *|- - + -------|| | |3 / 350 + ------------- *|- - + -------|| \/ 714 *cos|----------------| \/ 238 *sin|----------------|| \/ 238 *cos|----------------| \/ 714 *sin|----------------| 3 / 350 + -------------
2 \\/ 4 \ 2 2 // | \\/ 4 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 / 2 \\/ 4 \ 2 2 // | \\/ 4 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 / 2 119 \/ 4
- - - -------------------------------------------------- + I*|- -------------------------------------------------- + ----------------------------- + -----------------------------| - ----------------------------- + ----------------------------- + - - - -------------------------------------------------- + I*|- -------------------------------------------------- - ----------------------------- + -----------------------------| + ----------------------------- + ----------------------------- + - - - ---------------------------- - --------------------------
3 6 \ 6 12 12 / 12 12 3 6 \ 6 12 12 / 12 12 3 _____________________ 3
/ ______
/ 21*I*\/ 3198
6*3 / 350 + -------------
\/ 4
$$\left(\left(- \frac{2}{3} - \frac{\sqrt{714} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} - \frac{119 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6} + \frac{\sqrt{238} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + i \left(- \frac{119 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6} + \frac{\sqrt{238} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + \frac{\sqrt{714} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12}\right)\right) + \left(- \frac{2}{3} + \frac{\sqrt{714} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + \frac{\sqrt{238} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} - \frac{119 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6} + i \left(- \frac{\sqrt{714} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + \frac{\sqrt{238} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} - \frac{119 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6}\right)\right)\right) + \left(- \frac{2}{3} - \frac{\sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}{3} - \frac{119}{6 \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
119*re|------------------------------------------| 119*re|------------------------------------------| | 119*im|------------------------------------------| / / ______\\ / / ______\\| | 119*im|------------------------------------------| / / ______\\ / / ______\\| / / ______\\
| _____________________ | | _____________________ | _____________________ | | _____________________ | | |3*\/ 3198 || | |3*\/ 3198 ||| | | _____________________ | | |3*\/ 3198 || | |3*\/ 3198 ||| | |3*\/ 3198 ||
| / ______ / ___\| | / ______ / ___\| / ______ | | / ______ / ___\| |atan|----------|| |atan|----------||| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------||
| / 21*I*\/ 3198 | 1 I*\/ 3 || | / 21*I*\/ 3198 | 1 I*\/ 3 || / 21*I*\/ 3198 | | / 21*I*\/ 3198 | 1 I*\/ 3 || _____ | \ 200 /| _____ | \ 200 /|| | | / 21*I*\/ 3198 | 1 I*\/ 3 || _____ | \ 200 /| _____ | \ 200 /|| _____ | \ 200 /|
|3 / 350 + ------------- *|- - + -------|| |3 / 350 + ------------- *|- - - -------|| 3 / 350 + ------------- | |3 / 350 + ------------- *|- - + -------|| \/ 714 *cos|----------------| \/ 238 *sin|----------------|| | |3 / 350 + ------------- *|- - - -------|| \/ 238 *sin|----------------| \/ 714 *cos|----------------|| \/ 238 *cos|----------------|
119 \\/ 4 \ 2 2 // \\/ 4 \ 2 2 // \/ 4 | \\/ 4 \ 2 2 // \ 3 / \ 3 /| | \\/ 4 \ 2 2 // \ 3 / \ 3 /| \ 3 /
-2 - ---------------------------- - -------------------------------------------------- - -------------------------------------------------- - -------------------------- + I*|- -------------------------------------------------- - ----------------------------- + -----------------------------| + I*|- -------------------------------------------------- + ----------------------------- + -----------------------------| + -----------------------------
_____________________ 6 6 3 \ 6 12 12 / \ 6 12 12 / 6
/ ______
/ 21*I*\/ 3198
6*3 / 350 + -------------
\/ 4
$$-2 - \frac{119 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6} - \frac{119 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6} + \frac{\sqrt{238} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{6} - \frac{\sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}{3} + i \left(- \frac{\sqrt{714} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + \frac{\sqrt{238} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} - \frac{119 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6}\right) + i \left(- \frac{119 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6} + \frac{\sqrt{238} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + \frac{\sqrt{714} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12}\right) - \frac{119}{6 \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 119*re|------------------------------------------| | 119*im|------------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\| | 119*re|------------------------------------------| | 119*im|------------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\|
| | _____________________ | | | _____________________ | | |3*\/ 3198 || | |3*\/ 3198 ||| | |3*\/ 3198 || | |3*\/ 3198 ||| | | _____________________ | | | _____________________ | | |3*\/ 3198 || | |3*\/ 3198 ||| | |3*\/ 3198 || | |3*\/ 3198 ||| / _____________________\
| | / ______ / ___\| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | | / ______ / ___\| | | / ______ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | / ______ |
| | / 21*I*\/ 3198 | 1 I*\/ 3 || | | / 21*I*\/ 3198 | 1 I*\/ 3 || _____ | \ 200 /| _____ | \ 200 /|| _____ | \ 200 /| _____ | \ 200 /|| | | / 21*I*\/ 3198 | 1 I*\/ 3 || | | / 21*I*\/ 3198 | 1 I*\/ 3 || _____ | \ 200 /| _____ | \ 200 /|| _____ | \ 200 /| _____ | \ 200 /|| | / 21*I*\/ 3198 |
| |3 / 350 + ------------- *|- - - -------|| | |3 / 350 + ------------- *|- - - -------|| \/ 238 *sin|----------------| \/ 714 *cos|----------------|| \/ 714 *sin|----------------| \/ 238 *cos|----------------|| | |3 / 350 + ------------- *|- - + -------|| | |3 / 350 + ------------- *|- - + -------|| \/ 714 *cos|----------------| \/ 238 *sin|----------------|| \/ 238 *cos|----------------| \/ 714 *sin|----------------|| | 3 / 350 + ------------- |
| 2 \\/ 4 \ 2 2 // | \\/ 4 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /| | 2 \\/ 4 \ 2 2 // | \\/ 4 \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /| | 2 119 \/ 4 |
|- - - -------------------------------------------------- + I*|- -------------------------------------------------- + ----------------------------- + -----------------------------| - ----------------------------- + -----------------------------|*|- - - -------------------------------------------------- + I*|- -------------------------------------------------- - ----------------------------- + -----------------------------| + ----------------------------- + -----------------------------|*|- - - ---------------------------- - --------------------------|
\ 3 6 \ 6 12 12 / 12 12 / \ 3 6 \ 6 12 12 / 12 12 / | 3 _____________________ 3 |
| / ______ |
| / 21*I*\/ 3198 |
| 6*3 / 350 + ------------- |
\ \/ 4 /
$$\left(- \frac{2}{3} - \frac{\sqrt{714} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} - \frac{119 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6} + \frac{\sqrt{238} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + i \left(- \frac{119 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6} + \frac{\sqrt{238} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + \frac{\sqrt{714} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12}\right)\right) \left(- \frac{2}{3} + \frac{\sqrt{714} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + \frac{\sqrt{238} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} - \frac{119 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6} + i \left(- \frac{\sqrt{714} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} + \frac{\sqrt{238} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)}}{12} - \frac{119 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)}}{6}\right)\right) \left(- \frac{2}{3} - \frac{\sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}{3} - \frac{119}{6 \sqrt[3]{350 + \frac{21 \sqrt{3198} i}{4}}}\right)$$
=
/ / / ______\\ / / ______\\\
| | |3*\/ 3198 || | |3*\/ 3198 |||
/ ______________________ / ______________________\\ | |2*atan|----------|| |atan|----------|||
2/3 | 2/3 3 / ______ | 3 / ______ || | | \ 200 /| _____ | \ 200 /||
7 *\119*2 + \/ 1400 + 21*I*\/ 3198 *\4 + \/ 2800 + 42*I*\/ 3198 //*|222 - 476*cos|------------------| + 8*\/ 238 *cos|----------------||
\ \ 3 / \ 3 //
-------------------------------------------------------------------------------------------------------------------------------------------------
____________________
3 / ______
1512*\/ 200 + 3*I*\/ 3198
$$\frac{7^{\frac{2}{3}} \left(119 \cdot 2^{\frac{2}{3}} + \left(4 + \sqrt[3]{2800 + 42 \sqrt{3198} i}\right) \sqrt[3]{1400 + 21 \sqrt{3198} i}\right) \left(- 476 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)} + 8 \sqrt{238} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{3198}}{200} \right)}}{3} \right)} + 222\right)}{1512 \sqrt[3]{200 + 3 \sqrt{3198} i}}$$
7^(2/3)*(119*2^(2/3) + (1400 + 21*i*sqrt(3198))^(1/3)*(4 + (2800 + 42*i*sqrt(3198))^(1/3)))*(222 - 476*cos(2*atan(3*sqrt(3198)/200)/3) + 8*sqrt(238)*cos(atan(3*sqrt(3198)/200)/3))/(1512*(200 + 3*i*sqrt(3198))^(1/3))
Respuesta numérica
[src]
x1 = 2.86894210670733
x2 = 0.79940221017475
x3 = -5.66834431688208
x3 = -5.66834431688208