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(8*x^3)/3-3*x*x-12*x+10.95=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 8*x 219 ---- - 3*x*x - 12*x + --- = 0 3 20
$$\left(- 12 x + \left(- x 3 x + \frac{8 x^{3}}{3}\right)\right) + \frac{219}{20} = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(- 12 x + \left(- x 3 x + \frac{8 x^{3}}{3}\right)\right) + \frac{219}{20} = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - \frac{9 x^{2}}{8} - \frac{9 x}{2} + \frac{657}{160} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{9}{8}$$
$$q = \frac{c}{a}$$
$$q = - \frac{9}{2}$$
$$v = \frac{d}{a}$$
$$v = \frac{657}{160}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = \frac{9}{8}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{9}{2}$$
$$x_{1} x_{2} x_{3} = \frac{657}{160}$$
$$\left(- 12 x + \left(- x 3 x + \frac{8 x^{3}}{3}\right)\right) + \frac{219}{20} = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - \frac{9 x^{2}}{8} - \frac{9 x}{2} + \frac{657}{160} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{9}{8}$$
$$q = \frac{c}{a}$$
$$q = - \frac{9}{2}$$
$$v = \frac{d}{a}$$
$$v = \frac{657}{160}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = \frac{9}{8}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{9}{2}$$
$$x_{1} x_{2} x_{3} = \frac{657}{160}$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
315*re|---------------------------------------------| | 315*im|---------------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| ________________________| | | ________________________| | |4*\/ 2859 || | |4*\/ 2859 ||| | |4*\/ 2859 || | |4*\/ 2859 ||
|/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
|| 1 I*\/ 3 | / 79947 567*I*\/ 2859 | | || 1 I*\/ 3 | / 79947 567*I*\/ 2859 | _____ | \ 141 /| ____ | \ 141 /|| ____ | \ 141 /| _____ | \ 141 /|
||- - - -------|*3 / ----- + -------------- | | ||- - - -------|*3 / ----- + -------------- | \/ 105 *sin|----------------| 3*\/ 35 *cos|----------------|| 3*\/ 35 *sin|----------------| \/ 105 *cos|----------------|
3 \\ 2 2 / \/ 2560 640 / | \\ 2 2 / \/ 2560 640 / \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = - - ----------------------------------------------------- + I*|- ----------------------------------------------------- + ----------------------------- + ------------------------------| - ------------------------------ + -----------------------------
8 64 \ 64 16 16 / 16 16
$$x_{1} = - \frac{3 \sqrt{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} - \frac{315 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64} + \frac{3}{8} + \frac{\sqrt{105} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + i \left(- \frac{315 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64} + \frac{\sqrt{105} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + \frac{3 \sqrt{35} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16}\right)$$
/ 1 \ / / 1 \ \
315*re|---------------------------------------------| | 315*im|---------------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| ________________________| | | ________________________| | |4*\/ 2859 || | |4*\/ 2859 ||| | |4*\/ 2859 || | |4*\/ 2859 ||
|/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
|| 1 I*\/ 3 | / 79947 567*I*\/ 2859 | | || 1 I*\/ 3 | / 79947 567*I*\/ 2859 | ____ | \ 141 /| _____ | \ 141 /|| _____ | \ 141 /| ____ | \ 141 /|
||- - + -------|*3 / ----- + -------------- | | ||- - + -------|*3 / ----- + -------------- | 3*\/ 35 *cos|----------------| \/ 105 *sin|----------------|| \/ 105 *cos|----------------| 3*\/ 35 *sin|----------------|
3 \\ 2 2 / \/ 2560 640 / | \\ 2 2 / \/ 2560 640 / \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = - - ----------------------------------------------------- + I*|- ----------------------------------------------------- - ------------------------------ + -----------------------------| + ----------------------------- + ------------------------------
8 64 \ 64 16 16 / 16 16
$$x_{2} = \frac{3 \sqrt{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + \frac{3}{8} + \frac{\sqrt{105} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} - \frac{315 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64} + i \left(- \frac{3 \sqrt{35} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + \frac{\sqrt{105} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} - \frac{315 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64}\right)$$
________________________
/ ______
/ 79947 567*I*\/ 2859
3 / ----- + --------------
3 315 \/ 2560 640
x3 = - - -------------------------------- - -----------------------------
8 ________________________ 3
/ ______
/ 79947 567*I*\/ 2859
64*3 / ----- + --------------
\/ 2560 640
$$x_{3} = \frac{3}{8} - \frac{\sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}{3} - \frac{315}{64 \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}$$
x3 = 3/8 - (79947/2560 + 567*sqrt(2859)*i/640)^(1/3)/3 - 315/(64*(79947/2560 + 567*sqrt(2859)*i/640)^(1/3))
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
315*re|---------------------------------------------| | 315*im|---------------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\ 315*re|---------------------------------------------| | 315*im|---------------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| ________________________| | | ________________________| | |4*\/ 2859 || | |4*\/ 2859 ||| | |4*\/ 2859 || | |4*\/ 2859 || | ________________________| | | ________________________| | |4*\/ 2859 || | |4*\/ 2859 ||| | |4*\/ 2859 || | |4*\/ 2859 || ________________________
|/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| / ______
|| 1 I*\/ 3 | / 79947 567*I*\/ 2859 | | || 1 I*\/ 3 | / 79947 567*I*\/ 2859 | _____ | \ 141 /| ____ | \ 141 /|| ____ | \ 141 /| _____ | \ 141 /| || 1 I*\/ 3 | / 79947 567*I*\/ 2859 | | || 1 I*\/ 3 | / 79947 567*I*\/ 2859 | ____ | \ 141 /| _____ | \ 141 /|| _____ | \ 141 /| ____ | \ 141 /| / 79947 567*I*\/ 2859
||- - - -------|*3 / ----- + -------------- | | ||- - - -------|*3 / ----- + -------------- | \/ 105 *sin|----------------| 3*\/ 35 *cos|----------------|| 3*\/ 35 *sin|----------------| \/ 105 *cos|----------------| ||- - + -------|*3 / ----- + -------------- | | ||- - + -------|*3 / ----- + -------------- | 3*\/ 35 *cos|----------------| \/ 105 *sin|----------------|| \/ 105 *cos|----------------| 3*\/ 35 *sin|----------------| 3 / ----- + --------------
3 \\ 2 2 / \/ 2560 640 / | \\ 2 2 / \/ 2560 640 / \ 3 / \ 3 /| \ 3 / \ 3 / 3 \\ 2 2 / \/ 2560 640 / | \\ 2 2 / \/ 2560 640 / \ 3 / \ 3 /| \ 3 / \ 3 / 3 315 \/ 2560 640
- - ----------------------------------------------------- + I*|- ----------------------------------------------------- + ----------------------------- + ------------------------------| - ------------------------------ + ----------------------------- + - - ----------------------------------------------------- + I*|- ----------------------------------------------------- - ------------------------------ + -----------------------------| + ----------------------------- + ------------------------------ + - - -------------------------------- - -----------------------------
8 64 \ 64 16 16 / 16 16 8 64 \ 64 16 16 / 16 16 8 ________________________ 3
/ ______
/ 79947 567*I*\/ 2859
64*3 / ----- + --------------
\/ 2560 640
$$\left(\left(- \frac{3 \sqrt{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} - \frac{315 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64} + \frac{3}{8} + \frac{\sqrt{105} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + i \left(- \frac{315 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64} + \frac{\sqrt{105} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + \frac{3 \sqrt{35} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16}\right)\right) + \left(\frac{3 \sqrt{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + \frac{3}{8} + \frac{\sqrt{105} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} - \frac{315 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64} + i \left(- \frac{3 \sqrt{35} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + \frac{\sqrt{105} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} - \frac{315 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64}\right)\right)\right) + \left(\frac{3}{8} - \frac{\sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}{3} - \frac{315}{64 \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
315*re|---------------------------------------------| 315*re|---------------------------------------------| | 315*im|---------------------------------------------| / / ______\\ / / ______\\| | 315*im|---------------------------------------------| / / ______\\ / / ______\\| / / ______\\
| ________________________| | ________________________| ________________________ | | ________________________| | |4*\/ 2859 || | |4*\/ 2859 ||| | | ________________________| | |4*\/ 2859 || | |4*\/ 2859 ||| | |4*\/ 2859 ||
|/ ___\ / ______ | |/ ___\ / ______ | / ______ | |/ ___\ / ______ | |atan|----------|| |atan|----------||| | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------||
|| 1 I*\/ 3 | / 79947 567*I*\/ 2859 | || 1 I*\/ 3 | / 79947 567*I*\/ 2859 | / 79947 567*I*\/ 2859 | || 1 I*\/ 3 | / 79947 567*I*\/ 2859 | ____ | \ 141 /| _____ | \ 141 /|| | || 1 I*\/ 3 | / 79947 567*I*\/ 2859 | _____ | \ 141 /| ____ | \ 141 /|| _____ | \ 141 /|
||- - + -------|*3 / ----- + -------------- | ||- - - -------|*3 / ----- + -------------- | 3 / ----- + -------------- | ||- - + -------|*3 / ----- + -------------- | 3*\/ 35 *cos|----------------| \/ 105 *sin|----------------|| | ||- - - -------|*3 / ----- + -------------- | \/ 105 *sin|----------------| 3*\/ 35 *cos|----------------|| \/ 105 *cos|----------------|
9 315 \\ 2 2 / \/ 2560 640 / \\ 2 2 / \/ 2560 640 / \/ 2560 640 | \\ 2 2 / \/ 2560 640 / \ 3 / \ 3 /| | \\ 2 2 / \/ 2560 640 / \ 3 / \ 3 /| \ 3 /
- - -------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------- + I*|- ----------------------------------------------------- - ------------------------------ + -----------------------------| + I*|- ----------------------------------------------------- + ----------------------------- + ------------------------------| + -----------------------------
8 ________________________ 64 64 3 \ 64 16 16 / \ 64 16 16 / 8
/ ______
/ 79947 567*I*\/ 2859
64*3 / ----- + --------------
\/ 2560 640
$$- \frac{315 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64} - \frac{315 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64} + \frac{9}{8} + \frac{\sqrt{105} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{8} - \frac{\sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}{3} + i \left(- \frac{3 \sqrt{35} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + \frac{\sqrt{105} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} - \frac{315 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64}\right) + i \left(- \frac{315 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64} + \frac{\sqrt{105} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + \frac{3 \sqrt{35} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16}\right) - \frac{315}{64 \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 315*re|---------------------------------------------| | 315*im|---------------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\| | 315*re|---------------------------------------------| | 315*im|---------------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\|
| | ________________________| | | ________________________| | |4*\/ 2859 || | |4*\/ 2859 ||| | |4*\/ 2859 || | |4*\/ 2859 ||| | | ________________________| | | ________________________| | |4*\/ 2859 || | |4*\/ 2859 ||| | |4*\/ 2859 || | |4*\/ 2859 ||| / ________________________\
| |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | / ______ |
| || 1 I*\/ 3 | / 79947 567*I*\/ 2859 | | || 1 I*\/ 3 | / 79947 567*I*\/ 2859 | _____ | \ 141 /| ____ | \ 141 /|| ____ | \ 141 /| _____ | \ 141 /|| | || 1 I*\/ 3 | / 79947 567*I*\/ 2859 | | || 1 I*\/ 3 | / 79947 567*I*\/ 2859 | ____ | \ 141 /| _____ | \ 141 /|| _____ | \ 141 /| ____ | \ 141 /|| | / 79947 567*I*\/ 2859 |
| ||- - - -------|*3 / ----- + -------------- | | ||- - - -------|*3 / ----- + -------------- | \/ 105 *sin|----------------| 3*\/ 35 *cos|----------------|| 3*\/ 35 *sin|----------------| \/ 105 *cos|----------------|| | ||- - + -------|*3 / ----- + -------------- | | ||- - + -------|*3 / ----- + -------------- | 3*\/ 35 *cos|----------------| \/ 105 *sin|----------------|| \/ 105 *cos|----------------| 3*\/ 35 *sin|----------------|| | 3 / ----- + -------------- |
|3 \\ 2 2 / \/ 2560 640 / | \\ 2 2 / \/ 2560 640 / \ 3 / \ 3 /| \ 3 / \ 3 /| |3 \\ 2 2 / \/ 2560 640 / | \\ 2 2 / \/ 2560 640 / \ 3 / \ 3 /| \ 3 / \ 3 /| |3 315 \/ 2560 640 |
|- - ----------------------------------------------------- + I*|- ----------------------------------------------------- + ----------------------------- + ------------------------------| - ------------------------------ + -----------------------------|*|- - ----------------------------------------------------- + I*|- ----------------------------------------------------- - ------------------------------ + -----------------------------| + ----------------------------- + ------------------------------|*|- - -------------------------------- - -----------------------------|
\8 64 \ 64 16 16 / 16 16 / \8 64 \ 64 16 16 / 16 16 / |8 ________________________ 3 |
| / ______ |
| / 79947 567*I*\/ 2859 |
| 64*3 / ----- + -------------- |
\ \/ 2560 640 /
$$\left(- \frac{3 \sqrt{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} - \frac{315 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64} + \frac{3}{8} + \frac{\sqrt{105} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + i \left(- \frac{315 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64} + \frac{\sqrt{105} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + \frac{3 \sqrt{35} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16}\right)\right) \left(\frac{3 \sqrt{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + \frac{3}{8} + \frac{\sqrt{105} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} - \frac{315 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64} + i \left(- \frac{3 \sqrt{35} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} + \frac{\sqrt{105} \sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}}{16} - \frac{315 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)}}{64}\right)\right) \left(\frac{3}{8} - \frac{\sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}{3} - \frac{315}{64 \sqrt[3]{\frac{79947}{2560} + \frac{567 \sqrt{2859} i}{640}}}\right)$$
=
/ / / ______\\ / / ______\\\
| | |4*\/ 2859 || | |4*\/ 2859 |||
/ ______________________ / ______________________\\ | |2*atan|----------|| |atan|----------|||
2/3 | 3 ___ 3 / ______ | 2/3 3 / ______ || | | \ 141 /| _____ | \ 141 /||
-21 *\525*\/ 5 - \/ 2961 + 84*I*\/ 2859 *\15 - 5 *\/ 2961 + 84*I*\/ 2859 //*|-384 + 840*cos|------------------| + 24*\/ 105 *cos|----------------||
\ \ 3 / \ 3 //
-------------------------------------------------------------------------------------------------------------------------------------------------------------
____________________
3 / ______
215040*\/ 141 + 4*I*\/ 2859
$$- \frac{21^{\frac{2}{3}} \left(525 \sqrt[3]{5} - \left(15 - 5^{\frac{2}{3}} \sqrt[3]{2961 + 84 \sqrt{2859} i}\right) \sqrt[3]{2961 + 84 \sqrt{2859} i}\right) \left(-384 + 24 \sqrt{105} \cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)} + 840 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{4 \sqrt{2859}}{141} \right)}}{3} \right)}\right)}{215040 \sqrt[3]{141 + 4 \sqrt{2859} i}}$$
-21^(2/3)*(525*5^(1/3) - (2961 + 84*i*sqrt(2859))^(1/3)*(15 - 5^(2/3)*(2961 + 84*i*sqrt(2859))^(1/3)))*(-384 + 840*cos(2*atan(4*sqrt(2859)/141)/3) + 24*sqrt(105)*cos(atan(4*sqrt(2859)/141)/3))/(215040*(141 + 4*i*sqrt(2859))^(1/3))
Respuesta numérica
[src]
x1 = 0.869579813249455
x2 = 2.30450087483421
x3 = -2.04908068808366
x3 = -2.04908068808366