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Expresiones semejantes
- x^3-2*x^2+32*x+19=0
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-x^3-2*x^2+32*x+19=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 - x - 2*x + 32*x + 19 = 0
$$\left(32 x + \left(- x^{3} - 2 x^{2}\right)\right) + 19 = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(32 x + \left(- x^{3} - 2 x^{2}\right)\right) + 19 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + 2 x^{2} - 32 x - 19 = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = -32$$
$$v = \frac{d}{a}$$
$$v = -19$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -2$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -32$$
$$x_{1} x_{2} x_{3} = -19$$
$$\left(32 x + \left(- x^{3} - 2 x^{2}\right)\right) + 19 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + 2 x^{2} - 32 x - 19 = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = -32$$
$$v = \frac{d}{a}$$
$$v = -19$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -2$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -32$$
$$x_{1} x_{2} x_{3} = -19$$
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
100*re|------------------------------------------| / / ________\\ | 100*im|------------------------------------------| / / ________\\ / / ________\\| / / ________\\ 100*re|------------------------------------------| / / ________\\ | 100*im|------------------------------------------| / / ________\\ / / ________\\| / / ________\\
| _____________________| | |3*\/ 443751 || | | _____________________| | |3*\/ 443751 || | |3*\/ 443751 ||| | |3*\/ 443751 || | _____________________| | |3*\/ 443751 || | | _____________________| | |3*\/ 443751 || | |3*\/ 443751 ||| | |3*\/ 443751 || _____________________
|/ ___\ / ________ | |atan|------------|| | |/ ___\ / ________ | |atan|------------|| |atan|------------||| |atan|------------|| |/ ___\ / ________ | |atan|------------|| | |/ ___\ / ________ | |atan|------------|| |atan|------------||| |atan|------------|| / ________
|| 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| | || 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| ___ | \ 79 /|| ___ | \ 79 /| || 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| | || 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| ___ | \ 79 /|| ___ | \ 79 /| / 79 3*I*\/ 443751
||- - - -------|*3 / -- + -------------- | 5*cos|------------------| | ||- - - -------|*3 / -- + -------------- | 5*sin|------------------| 5*\/ 3 *cos|------------------|| 5*\/ 3 *sin|------------------| ||- - + -------|*3 / -- + -------------- | 5*cos|------------------| | ||- - + -------|*3 / -- + -------------- | 5*sin|------------------| 5*\/ 3 *cos|------------------|| 5*\/ 3 *sin|------------------| 3 / -- + --------------
2 \\ 2 2 / \/ 2 2 / \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 / 2 \\ 2 2 / \/ 2 2 / \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 / 2 100 \/ 2 2
- - - -------------------------------------------------- + ------------------------- + I*|- -------------------------------------------------- + ------------------------- + -------------------------------| - ------------------------------- + - - - -------------------------------------------------- + ------------------------- + I*|- -------------------------------------------------- + ------------------------- - -------------------------------| + ------------------------------- + - - - ---------------------------- - --------------------------
3 3 3 \ 3 3 3 / 3 3 3 3 \ 3 3 3 / 3 3 _____________________ 3
/ ________
/ 79 3*I*\/ 443751
3*3 / -- + --------------
\/ 2 2
$$\left(\left(- \frac{2}{3} + \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} - \frac{100 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3} + i \left(- \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} - \frac{100 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3}\right)\right) + \left(- \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} - \frac{2}{3} - \frac{100 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3} + \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + i \left(- \frac{100 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3} + \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3}\right)\right)\right) + \left(- \frac{2}{3} - \frac{\sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}{3} - \frac{100}{3 \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
100*re|------------------------------------------| 100*re|------------------------------------------| / / ________\\ | 100*im|------------------------------------------| / / ________\\ / / ________\\| | 100*im|------------------------------------------| / / ________\\ / / ________\\|
| _____________________| | _____________________| _____________________ | |3*\/ 443751 || | | _____________________| | |3*\/ 443751 || | |3*\/ 443751 ||| | | _____________________| | |3*\/ 443751 || | |3*\/ 443751 |||
|/ ___\ / ________ | |/ ___\ / ________ | / ________ |atan|------------|| | |/ ___\ / ________ | |atan|------------|| |atan|------------||| | |/ ___\ / ________ | |atan|------------|| |atan|------------|||
|| 1 I*\/ 3 | / 79 3*I*\/ 443751 | || 1 I*\/ 3 | / 79 3*I*\/ 443751 | / 79 3*I*\/ 443751 | \ 79 /| | || 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| ___ | \ 79 /|| | || 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| ___ | \ 79 /||
||- - + -------|*3 / -- + -------------- | ||- - - -------|*3 / -- + -------------- | 3 / -- + -------------- 10*cos|------------------| | ||- - + -------|*3 / -- + -------------- | 5*sin|------------------| 5*\/ 3 *cos|------------------|| | ||- - - -------|*3 / -- + -------------- | 5*sin|------------------| 5*\/ 3 *cos|------------------||
100 \\ 2 2 / \/ 2 2 / \\ 2 2 / \/ 2 2 / \/ 2 2 \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /|
-2 - ---------------------------- - -------------------------------------------------- - -------------------------------------------------- - -------------------------- + -------------------------- + I*|- -------------------------------------------------- + ------------------------- - -------------------------------| + I*|- -------------------------------------------------- + ------------------------- + -------------------------------|
_____________________ 3 3 3 3 \ 3 3 3 / \ 3 3 3 /
/ ________
/ 79 3*I*\/ 443751
3*3 / -- + --------------
\/ 2 2
$$-2 - \frac{100 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3} - \frac{100 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3} + \frac{10 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} - \frac{\sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}{3} + i \left(- \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} - \frac{100 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3}\right) + i \left(- \frac{100 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3} + \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3}\right) - \frac{100}{3 \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 100*re|------------------------------------------| / / ________\\ | 100*im|------------------------------------------| / / ________\\ / / ________\\| / / ________\\| | 100*re|------------------------------------------| / / ________\\ | 100*im|------------------------------------------| / / ________\\ / / ________\\| / / ________\\|
| | _____________________| | |3*\/ 443751 || | | _____________________| | |3*\/ 443751 || | |3*\/ 443751 ||| | |3*\/ 443751 ||| | | _____________________| | |3*\/ 443751 || | | _____________________| | |3*\/ 443751 || | |3*\/ 443751 ||| | |3*\/ 443751 ||| / _____________________\
| |/ ___\ / ________ | |atan|------------|| | |/ ___\ / ________ | |atan|------------|| |atan|------------||| |atan|------------||| | |/ ___\ / ________ | |atan|------------|| | |/ ___\ / ________ | |atan|------------|| |atan|------------||| |atan|------------||| | / ________ |
| || 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| | || 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| ___ | \ 79 /|| ___ | \ 79 /|| | || 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| | || 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| ___ | \ 79 /|| ___ | \ 79 /|| | / 79 3*I*\/ 443751 |
| ||- - - -------|*3 / -- + -------------- | 5*cos|------------------| | ||- - - -------|*3 / -- + -------------- | 5*sin|------------------| 5*\/ 3 *cos|------------------|| 5*\/ 3 *sin|------------------|| | ||- - + -------|*3 / -- + -------------- | 5*cos|------------------| | ||- - + -------|*3 / -- + -------------- | 5*sin|------------------| 5*\/ 3 *cos|------------------|| 5*\/ 3 *sin|------------------|| | 3 / -- + -------------- |
| 2 \\ 2 2 / \/ 2 2 / \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 /| | 2 \\ 2 2 / \/ 2 2 / \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 /| | 2 100 \/ 2 2 |
|- - - -------------------------------------------------- + ------------------------- + I*|- -------------------------------------------------- + ------------------------- + -------------------------------| - -------------------------------|*|- - - -------------------------------------------------- + ------------------------- + I*|- -------------------------------------------------- + ------------------------- - -------------------------------| + -------------------------------|*|- - - ---------------------------- - --------------------------|
\ 3 3 3 \ 3 3 3 / 3 / \ 3 3 3 \ 3 3 3 / 3 / | 3 _____________________ 3 |
| / ________ |
| / 79 3*I*\/ 443751 |
| 3*3 / -- + -------------- |
\ \/ 2 2 /
$$\left(- \frac{2}{3} + \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} - \frac{100 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3} + i \left(- \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} - \frac{100 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3}\right)\right) \left(- \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} - \frac{2}{3} - \frac{100 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3} + \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + i \left(- \frac{100 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3} + \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3}\right)\right) \left(- \frac{2}{3} - \frac{\sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}{3} - \frac{100}{3 \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)$$
=
/ / / ________\\ / / ________\\\
| | |3*\/ 443751 || | |3*\/ 443751 |||
/ _____________________ / _____________________\\ | |2*atan|------------|| |atan|------------|||
| 3 ___ 3 / ________ | 2/3 3 / ________ || | | \ 79 /| | \ 79 /||
\200*\/ 2 + \/ 79 + 3*I*\/ 443751 *\4 + 2 *\/ 79 + 3*I*\/ 443751 //*|96 - 200*cos|--------------------| + 40*cos|------------------||
\ \ 3 / \ 3 //
--------------------------------------------------------------------------------------------------------------------------------------------
_____________________
3 / ________
54*\/ 79 + 3*I*\/ 443751
$$\frac{\left(200 \sqrt[3]{2} + \left(4 + 2^{\frac{2}{3}} \sqrt[3]{79 + 3 \sqrt{443751} i}\right) \sqrt[3]{79 + 3 \sqrt{443751} i}\right) \left(- 200 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)} + 40 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)} + 96\right)}{54 \sqrt[3]{79 + 3 \sqrt{443751} i}}$$
(200*2^(1/3) + (79 + 3*i*sqrt(443751))^(1/3)*(4 + 2^(2/3)*(79 + 3*i*sqrt(443751))^(1/3)))*(96 - 200*cos(2*atan(3*sqrt(443751)/79)/3) + 40*cos(atan(3*sqrt(443751)/79)/3))/(54*(79 + 3*i*sqrt(443751))^(1/3))
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
100*re|------------------------------------------| / / ________\\ | 100*im|------------------------------------------| / / ________\\ / / ________\\| / / ________\\
| _____________________| | |3*\/ 443751 || | | _____________________| | |3*\/ 443751 || | |3*\/ 443751 ||| | |3*\/ 443751 ||
|/ ___\ / ________ | |atan|------------|| | |/ ___\ / ________ | |atan|------------|| |atan|------------||| |atan|------------||
|| 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| | || 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| ___ | \ 79 /|| ___ | \ 79 /|
||- - - -------|*3 / -- + -------------- | 5*cos|------------------| | ||- - - -------|*3 / -- + -------------- | 5*sin|------------------| 5*\/ 3 *cos|------------------|| 5*\/ 3 *sin|------------------|
2 \\ 2 2 / \/ 2 2 / \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 /
x1 = - - - -------------------------------------------------- + ------------------------- + I*|- -------------------------------------------------- + ------------------------- + -------------------------------| - -------------------------------
3 3 3 \ 3 3 3 / 3
$$x_{1} = - \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} - \frac{2}{3} - \frac{100 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3} + \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + i \left(- \frac{100 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3} + \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3}\right)$$
/ 1 \ / / 1 \ \
100*re|------------------------------------------| / / ________\\ | 100*im|------------------------------------------| / / ________\\ / / ________\\| / / ________\\
| _____________________| | |3*\/ 443751 || | | _____________________| | |3*\/ 443751 || | |3*\/ 443751 ||| | |3*\/ 443751 ||
|/ ___\ / ________ | |atan|------------|| | |/ ___\ / ________ | |atan|------------|| |atan|------------||| |atan|------------||
|| 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| | || 1 I*\/ 3 | / 79 3*I*\/ 443751 | | \ 79 /| ___ | \ 79 /|| ___ | \ 79 /|
||- - + -------|*3 / -- + -------------- | 5*cos|------------------| | ||- - + -------|*3 / -- + -------------- | 5*sin|------------------| 5*\/ 3 *cos|------------------|| 5*\/ 3 *sin|------------------|
2 \\ 2 2 / \/ 2 2 / \ 3 / | \\ 2 2 / \/ 2 2 / \ 3 / \ 3 /| \ 3 /
x2 = - - - -------------------------------------------------- + ------------------------- + I*|- -------------------------------------------------- + ------------------------- - -------------------------------| + -------------------------------
3 3 3 \ 3 3 3 / 3
$$x_{2} = - \frac{2}{3} + \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} - \frac{100 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3} + i \left(- \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} + \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{443751}}{79} \right)}}{3} \right)}}{3} - \frac{100 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}\right)}}{3}\right)$$
_____________________
/ ________
/ 79 3*I*\/ 443751
3 / -- + --------------
2 100 \/ 2 2
x3 = - - - ---------------------------- - --------------------------
3 _____________________ 3
/ ________
/ 79 3*I*\/ 443751
3*3 / -- + --------------
\/ 2 2
$$x_{3} = - \frac{2}{3} - \frac{\sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}{3} - \frac{100}{3 \sqrt[3]{\frac{79}{2} + \frac{3 \sqrt{443751} i}{2}}}$$
x3 = -2/3 - (79/2 + 3*sqrt(443751)*i/2)^(1/3)/3 - 100/(3*(79/2 + 3*sqrt(443751)*i/2)^(1/3))
Respuesta numérica
[src]
x1 = -0.578868585135325
x2 = -6.48356769565241
x3 = 5.06243628078773
x3 = 5.06243628078773