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La ecuación:
Ecuación x+3=-9*x
Ecuación x+3=-9x
Ecuación 5-2*(x-1)=4-x
Ecuación (x-5)^2=(x-8)^2
Expresar {x} en función de y en la ecuación:
12*x+14*y=-15
-19*x+1*y=0
7*x-19*y=-8
9*x+18*y=3
Expresiones idénticas
6x^ dos *sqrt(x)+ cinco = cero
6x al cuadrado multiplicar por raíz cuadrada de (x) más 5 es igual a 0
6x en el grado dos multiplicar por raíz cuadrada de (x) más cinco es igual a cero
6x^2*√(x)+5=0
6x2*sqrt(x)+5=0
6x2*sqrtx+5=0
6x²*sqrt(x)+5=0
6x en el grado 2*sqrt(x)+5=0
6x^2sqrt(x)+5=0
6x2sqrt(x)+5=0
6x2sqrtx+5=0
6x^2sqrtx+5=0
6x^2*sqrt(x)+5=O
Expresiones semejantes
6x^2*sqrt(x)-5=0
Expresiones con funciones
Raíz cuadrada sqrt
sqrt(x^2-4)+sqrt(x^2+x-2)=0
sqrt(x)=-49
sqrt(x+1)=1-x
sqrt(5+|x-2|)=1-x
sqrt(x-3)+sqrt(2-x)=3

6x^2*sqrt(x)+5=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

   2   ___        
6*x *\/ x  + 5 = 0

\sqrt{x} 6 x^{2} + 5 = 0

Simplificar

Solución detallada

Tenemos la ecuación

\sqrt{x} 6 x^{2} + 5 = 0

Ya que la potencia en la ecuación es igual a = 5/2 y miembro libre = -5 < 0,
significa que la ecuación correspondiente no tiene soluciones reales

Las demás 4 raíces son complejas.
hacemos el cambio:

z = x

entonces la ecuación será así:

z^{\frac{5}{2}} = - \frac{5}{6}

Cualquier número complejo se puede presentar que:

z = r e^{i p}

sustituimos en la ecuación

\left(r e^{i p}\right)^{\frac{5}{2}} = - \frac{5}{6}

donde

r = \frac{5^{\frac{2}{5}} \cdot 6^{\frac{3}{5}}}{6}

- módulo del número complejo
Sustituyamos r:

e^{\frac{5 i p}{2}} = -1

Usando la fórmula de Euler hallemos las raíces para p

i \sin{\left(\frac{5 p}{2} \right)} + \cos{\left(\frac{5 p}{2} \right)} = -1

es decir

\cos{\left(\frac{5 p}{2} \right)} = -1

\sin{\left(\frac{5 p}{2} \right)} = 0

entonces

p = \frac{4 \pi N}{5} + \frac{2 \pi}{5}

donde N=0,1,2,3,...
Seleccionando los valores de N y sustituyendo p en la fórmula para z
Es decir, la solución será para z:

z_{1} = \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6}\right)^{2}

z_{2} = \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} - \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}\right)^{2}

z_{3} = \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} - \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24}\right)^{2}

z_{4} = \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24}\right)^{2}

hacemos cambio inverso

z = x

x = z

Entonces la respuesta definitiva es:

x_{1} = \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6}\right)^{2}

x_{2} = \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} - \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}\right)^{2}

x_{3} = \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} - \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24}\right)^{2}

x_{4} = \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24}\right)^{2}

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

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                         2    2/5  3/5 |5   \/ 5 |     5 ___  4/5    /  5   \/ 5   |\/ 5 *6      5    *6   |                              2   |  5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |                                    |  5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |   |             5 ___  4/5    /  5   \/ 5      /  5   \/ 5  |    |  5 ___  4/5    /  5   \/ 5     5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |        |             5 ___  4/5    /  5   \/ 5      /  5   \/ 5  | |  5 ___  4/5    /  5   \/ 5     5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |   |             5 ___  4/5    /  5   \/ 5      /  5   \/ 5  |    |  5 ___  4/5    /  5   \/ 5     5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |        |             5 ___  4/5    /  5   \/ 5      /  5   \/ 5  | |  5 ___  4/5    /  5   \/ 5     5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |
/5 ___  4/5    7/10  4/5\    5   *6   *|- - -----|   I*\/ 5 *6   *  /   - - ----- *|---------- + ----------|   /   7/10  4/5   5 ___  4/5\    |  \/ 5 *6   *  /   - - -----    5    *6   *  /   - - ----- |        /   7/10  4/5   5 ___  4/5\ |  \/ 5 *6   *  /   - - -----    5    *6   *  /   - - ----- |   |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- |    |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - + -----    5    *6   *  /   - - ----- |        |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- | |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - + -----    5    *6   *  /   - - ----- |   |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- |    |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - - -----    5    *6   *  /   - + ----- |        |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- | |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - - -----    5    *6   *  /   - + ----- |
|\/ 5 *6      5    *6   |              \8     8  /                \/    8     8    \    24           24    /   |  5    *6      \/ 5 *6   |    |             \/    8     8                 \/    8     8   |        |  5    *6      \/ 5 *6   | |             \/    8     8                 \/    8     8   |   |\/ 5 *6                 \/    8     8    \/    8     8   |    |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |        |\/ 5 *6                 \/    8     8    \/    8     8   | |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |   |\/ 5 *6                 \/    8     8    \/    8     8   |    |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |        |\/ 5 *6                 \/    8     8    \/    8     8   | |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |
|---------- + ----------|  - --------------------- + ------------------------------------------------------- + |- ---------- + ----------|  - |- --------------------------- - ---------------------------|  + 2*I*|- ---------- + ----------|*|- --------------------------- - ---------------------------| + |---------- + --------------------------------------------|  - |- --------------------------- - --------------------------- - --------------------------- + ---------------------------|  + 2*I*|---------- + --------------------------------------------|*|- --------------------------- - --------------------------- - --------------------------- + ---------------------------| + |---------- - --------------------------------------------|  - |- --------------------------- + --------------------------- + --------------------------- + ---------------------------|  + 2*I*|---------- - --------------------------------------------|*|- --------------------------- + --------------------------- + --------------------------- + ---------------------------|
\    24           24    /              6                                        3                              \      24           24    /    \               12                            12            /        \      24           24    / \               12                            12            /   \    24                            6                      /    \               24                            24                            24                            24            /        \    24                            6                      / \               24                            24                            24                            24            /   \    24                            6                      /    \               24                            24                            24                            24            /        \    24                            6                      / \               24                            24                            24                            24            /

\left(- \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24}\right)^{2} + \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right)^{2} + 2 i \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right) \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24}\right)\right) + \left(\left(- \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24}\right)^{2} + \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6}\right)^{2} + 2 i \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6}\right) \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24}\right)\right) + \left(\left(- \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}\right)^{2} + \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right)^{2} + 2 i \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right) \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}\right)\right) + \left(- \frac{5^{\frac{2}{5}} \cdot 6^{\frac{3}{5}} \left(\frac{5}{8} - \frac{\sqrt{5}}{8}\right)}{6} + \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24}\right)^{2} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24}\right)}{3}\right)\right)\right)

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/   7/10  4/5   5 ___  4/5\    /5 ___  4/5    7/10  4/5\    |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- |    |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- |    |  \/ 5 *6   *  /   - - -----    5    *6   *  /   - - ----- |    |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - + -----    5    *6   *  /   - - ----- |    |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - - -----    5    *6   *  /   - + ----- |        /   7/10  4/5   5 ___  4/5\ |  \/ 5 *6   *  /   - - -----    5    *6   *  /   - - ----- |       |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- | |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - - -----    5    *6   *  /   - + ----- |       |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- | |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - + -----    5    *6   *  /   - - ----- |   5   *6   *|- - -----|   I*\/ 5 *6   *  /   - - ----- *|---------- + ----------|
|  5    *6      \/ 5 *6   |    |\/ 5 *6      5    *6   |    |\/ 5 *6                 \/    8     8    \/    8     8   |    |\/ 5 *6                 \/    8     8    \/    8     8   |    |             \/    8     8                 \/    8     8   |    |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |    |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |        |  5    *6      \/ 5 *6   | |             \/    8     8                 \/    8     8   |       |\/ 5 *6                 \/    8     8    \/    8     8   | |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |       |\/ 5 *6                 \/    8     8    \/    8     8   | |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |             \8     8  /                \/    8     8    \    24           24    /
|- ---------- + ----------|  + |---------- + ----------|  + |---------- - --------------------------------------------|  + |---------- + --------------------------------------------|  - |- --------------------------- - ---------------------------|  - |- --------------------------- - --------------------------- - --------------------------- + ---------------------------|  - |- --------------------------- + --------------------------- + --------------------------- + ---------------------------|  + 2*I*|- ---------- + ----------|*|- --------------------------- - ---------------------------| + 2*I*|---------- - --------------------------------------------|*|- --------------------------- + --------------------------- + --------------------------- + ---------------------------| + 2*I*|---------- + --------------------------------------------|*|- --------------------------- - --------------------------- - --------------------------- + ---------------------------| - --------------------- + -------------------------------------------------------
\      24           24    /    \    24           24    /    \    24                            6                      /    \    24                            6                      /    \               12                            12            /    \               24                            24                            24                            24            /    \               24                            24                            24                            24            /        \      24           24    / \               12                            12            /       \    24                            6                      / \               24                            24                            24                            24            /       \    24                            6                      / \               24                            24                            24                            24            /             6                                        3

- \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}\right)^{2} - \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24}\right)^{2} - \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24}\right)^{2} - \frac{5^{\frac{2}{5}} \cdot 6^{\frac{3}{5}} \left(\frac{5}{8} - \frac{\sqrt{5}}{8}\right)}{6} + \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right)^{2} + \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right)^{2} + \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24}\right)^{2} + \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6}\right)^{2} + 2 i \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6}\right) \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24}\right) + 2 i \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right) \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24}\right) + 2 i \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right) \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}\right) + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24}\right)}{3}

producto

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/                                                                       ___________                          \ |                               /                  ___________                   ___________\                                    /                  ___________                   ___________\| |/                             ___________      ___________\    /                  ___________                   ___________                   ___________                   ___________\        /                             ___________      ___________\ /                  ___________                   ___________                   ___________                   ___________\| |/                             ___________      ___________\    /                  ___________                   ___________                   ___________                   ___________\        /                             ___________      ___________\ /                  ___________                   ___________                   ___________                   ___________\|
|                                       /      ___\                    /       ___  /5 ___  4/5    7/10  4/5\| |                               |                 /       ___                   /       ___ |                                    |                 /       ___                   /       ___ || ||                            /       ___      /       ___ |    |                 /       ___                   /       ___                   /       ___                   /       ___ |        |                            /       ___      /       ___ | |                 /       ___                   /       ___                   /       ___                   /       ___ || ||                            /       ___      /       ___ |    |                 /       ___                   /       ___                   /       ___                   /       ___ |        |                            /       ___      /       ___ | |                 /       ___                   /       ___                   /       ___                   /       ___ ||
|                         2    2/5  3/5 |5   \/ 5 |     5 ___  4/5    /  5   \/ 5   |\/ 5 *6      5    *6   || |                           2   |  5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |                                    |  5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  || ||             5 ___  4/5    /  5   \/ 5      /  5   \/ 5  |    |  5 ___  4/5    /  5   \/ 5     5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |        |             5 ___  4/5    /  5   \/ 5      /  5   \/ 5  | |  5 ___  4/5    /  5   \/ 5     5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  || ||             5 ___  4/5    /  5   \/ 5      /  5   \/ 5  |    |  5 ___  4/5    /  5   \/ 5     5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |        |             5 ___  4/5    /  5   \/ 5      /  5   \/ 5  | |  5 ___  4/5    /  5   \/ 5     5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  ||
|/5 ___  4/5    7/10  4/5\    5   *6   *|- - -----|   I*\/ 5 *6   *  /   - - ----- *|---------- + ----------|| |/   7/10  4/5   5 ___  4/5\    |  \/ 5 *6   *  /   - - -----    5    *6   *  /   - - ----- |        /   7/10  4/5   5 ___  4/5\ |  \/ 5 *6   *  /   - - -----    5    *6   *  /   - - ----- || ||5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- |    |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - + -----    5    *6   *  /   - - ----- |        |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- | |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - + -----    5    *6   *  /   - - ----- || ||5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- |    |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - - -----    5    *6   *  /   - + ----- |        |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- | |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - - -----    5    *6   *  /   - + ----- ||
||\/ 5 *6      5    *6   |              \8     8  /                \/    8     8    \    24           24    /| ||  5    *6      \/ 5 *6   |    |             \/    8     8                 \/    8     8   |        |  5    *6      \/ 5 *6   | |             \/    8     8                 \/    8     8   || ||\/ 5 *6                 \/    8     8    \/    8     8   |    |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |        |\/ 5 *6                 \/    8     8    \/    8     8   | |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   || ||\/ 5 *6                 \/    8     8    \/    8     8   |    |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |        |\/ 5 *6                 \/    8     8    \/    8     8   | |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   ||
||---------- + ----------|  - --------------------- + -------------------------------------------------------|*||- ---------- + ----------|  - |- --------------------------- - ---------------------------|  + 2*I*|- ---------- + ----------|*|- --------------------------- - ---------------------------||*||---------- + --------------------------------------------|  - |- --------------------------- - --------------------------- - --------------------------- + ---------------------------|  + 2*I*|---------- + --------------------------------------------|*|- --------------------------- - --------------------------- - --------------------------- + ---------------------------||*||---------- - --------------------------------------------|  - |- --------------------------- + --------------------------- + --------------------------- + ---------------------------|  + 2*I*|---------- - --------------------------------------------|*|- --------------------------- + --------------------------- + --------------------------- + ---------------------------||
\\    24           24    /              6                                        3                           / \\      24           24    /    \               12                            12            /        \      24           24    / \               12                            12            // \\    24                            6                      /    \               24                            24                            24                            24            /        \    24                            6                      / \               24                            24                            24                            24            // \\    24                            6                      /    \               24                            24                            24                            24            /        \    24                            6                      / \               24                            24                            24                            24            //

\left(- \frac{5^{\frac{2}{5}} \cdot 6^{\frac{3}{5}} \left(\frac{5}{8} - \frac{\sqrt{5}}{8}\right)}{6} + \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24}\right)^{2} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24}\right)}{3}\right) \left(- \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}\right)^{2} + \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right)^{2} + 2 i \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right) \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}\right)\right) \left(- \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24}\right)^{2} + \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6}\right)^{2} + 2 i \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6}\right) \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24}\right)\right) \left(- \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24}\right)^{2} + \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right)^{2} + 2 i \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right) \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24}\right)\right)

                                                           ____________                           ___________                            ___________
     2/5 5 _____         3/5  2/5       9/10  2/5 10___   /        ___          9/10  2/5  3/5   /       ___          9/10  2/5 10___   /       ___ 
  5*3   *\/ 500    1325*5   *6      25*2    *3   *\/ 5 *\/  -5 + \/ 5     25*I*2    *3   *5   *\/  5 + \/ 5     25*I*2    *3   *\/ 5 *\/  5 + \/ 5  
- -------------- + -------------- + ----------------------------------- - ----------------------------------- + ------------------------------------
       1024             9216                        1152                                  2304                                  2304

- \frac{5 \cdot 3^{\frac{2}{5}} \sqrt[5]{500}}{1024} + \frac{1325 \cdot 5^{\frac{3}{5}} \cdot 6^{\frac{2}{5}}}{9216} - \frac{25 \cdot 2^{\frac{9}{10}} \cdot 3^{\frac{2}{5}} \cdot 5^{\frac{3}{5}} i \sqrt{\sqrt{5} + 5}}{2304} + \frac{25 \cdot 2^{\frac{9}{10}} \cdot 3^{\frac{2}{5}} \sqrt[10]{5} i \sqrt{\sqrt{5} + 5}}{2304} + \frac{25 \cdot 2^{\frac{9}{10}} \cdot 3^{\frac{2}{5}} \sqrt[10]{5} \sqrt{-5 + \sqrt{5}}}{1152}

-5*3^(2/5)*500^(1/5)/1024 + 1325*5^(3/5)*6^(2/5)/9216 + 25*2^(9/10)*3^(2/5)*5^(1/10)*sqrt(-5 + sqrt(5))/1152 - 25*i*2^(9/10)*3^(2/5)*5^(3/5)*sqrt(5 + sqrt(5))/2304 + 25*i*2^(9/10)*3^(2/5)*5^(1/10)*sqrt(5 + sqrt(5))/2304

Respuesta rápida [src]

                                                                            ___________                          
                                            /      ___\                    /       ___  /5 ___  4/5    7/10  4/5\
                              2    2/5  3/5 |5   \/ 5 |     5 ___  4/5    /  5   \/ 5   |\/ 5 *6      5    *6   |
     /5 ___  4/5    7/10  4/5\    5   *6   *|- - -----|   I*\/ 5 *6   *  /   - - ----- *|---------- + ----------|
     |\/ 5 *6      5    *6   |              \8     8  /                \/    8     8    \    24           24    /
x1 = |---------- + ----------|  - --------------------- + -------------------------------------------------------
     \    24           24    /              6                                        3

x_{1} = - \frac{5^{\frac{2}{5}} \cdot 6^{\frac{3}{5}} \left(\frac{5}{8} - \frac{\sqrt{5}}{8}\right)}{6} + \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24}\right)^{2} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24}\right)}{3}

                                                                                                 2                                                                                                
                                    /                  ___________                   ___________\                                    /                  ___________                   ___________\
                                    |                 /       ___                   /       ___ |                                    |                 /       ___                   /       ___ |
                                2   |  5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |                                    |  5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |
     /   7/10  4/5   5 ___  4/5\    |  \/ 5 *6   *  /   - - -----    5    *6   *  /   - - ----- |        /   7/10  4/5   5 ___  4/5\ |  \/ 5 *6   *  /   - - -----    5    *6   *  /   - - ----- |
     |  5    *6      \/ 5 *6   |    |             \/    8     8                 \/    8     8   |        |  5    *6      \/ 5 *6   | |             \/    8     8                 \/    8     8   |
x2 = |- ---------- + ----------|  - |- --------------------------- - ---------------------------|  + 2*I*|- ---------- + ----------|*|- --------------------------- - ---------------------------|
     \      24           24    /    \               12                            12            /        \      24           24    / \               12                            12            /

x_{2} = - \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}\right)^{2} + \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right)^{2} + 2 i \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right) \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}\right)

                                                                2                                                                                                                            2                                                                                                                                                                                            
     /                             ___________      ___________\    /                  ___________                   ___________                   ___________                   ___________\        /                             ___________      ___________\ /                  ___________                   ___________                   ___________                   ___________\
     |                            /       ___      /       ___ |    |                 /       ___                   /       ___                   /       ___                   /       ___ |        |                            /       ___      /       ___ | |                 /       ___                   /       ___                   /       ___                   /       ___ |
     |             5 ___  4/5    /  5   \/ 5      /  5   \/ 5  |    |  5 ___  4/5    /  5   \/ 5     5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |        |             5 ___  4/5    /  5   \/ 5      /  5   \/ 5  | |  5 ___  4/5    /  5   \/ 5     5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |
     |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- |    |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - + -----    5    *6   *  /   - - ----- |        |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- | |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - + -----    5    *6   *  /   - - ----- |
     |\/ 5 *6                 \/    8     8    \/    8     8   |    |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |        |\/ 5 *6                 \/    8     8    \/    8     8   | |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |
x3 = |---------- + --------------------------------------------|  - |- --------------------------- - --------------------------- - --------------------------- + ---------------------------|  + 2*I*|---------- + --------------------------------------------|*|- --------------------------- - --------------------------- - --------------------------- + ---------------------------|
     \    24                            6                      /    \               24                            24                            24                            24            /        \    24                            6                      / \               24                            24                            24                            24            /

x_{3} = - \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24}\right)^{2} + \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6}\right)^{2} + 2 i \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6}\right) \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24}\right)

                                                                2                                                                                                                            2                                                                                                                                                                                            
     /                             ___________      ___________\    /                  ___________                   ___________                   ___________                   ___________\        /                             ___________      ___________\ /                  ___________                   ___________                   ___________                   ___________\
     |                            /       ___      /       ___ |    |                 /       ___                   /       ___                   /       ___                   /       ___ |        |                            /       ___      /       ___ | |                 /       ___                   /       ___                   /       ___                   /       ___ |
     |             5 ___  4/5    /  5   \/ 5      /  5   \/ 5  |    |  5 ___  4/5    /  5   \/ 5     5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |        |             5 ___  4/5    /  5   \/ 5      /  5   \/ 5  | |  5 ___  4/5    /  5   \/ 5     5 ___  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5      7/10  4/5    /  5   \/ 5  |
     |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- |    |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - - -----    5    *6   *  /   - + ----- |        |5 ___  4/5   \/ 5 *6   *  /   - - ----- *  /   - + ----- | |  \/ 5 *6   *  /   - - -----    \/ 5 *6   *  /   - + -----    5    *6   *  /   - - -----    5    *6   *  /   - + ----- |
     |\/ 5 *6                 \/    8     8    \/    8     8   |    |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |        |\/ 5 *6                 \/    8     8    \/    8     8   | |             \/    8     8                 \/    8     8                 \/    8     8                 \/    8     8   |
x4 = |---------- - --------------------------------------------|  - |- --------------------------- + --------------------------- + --------------------------- + ---------------------------|  + 2*I*|---------- - --------------------------------------------|*|- --------------------------- + --------------------------- + --------------------------- + ---------------------------|
     \    24                            6                      /    \               24                            24                            24                            24            /        \    24                            6                      / \               24                            24                            24                            24            /

x_{4} = - \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24}\right)^{2} + \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right)^{2} + 2 i \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24}\right) \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24}\right)

x4 = -(-5^(1/5)*6^(4/5)*sqrt(5/8 - sqrt(5)/8)/24 + 5^(1/5)*6^(4/5)*sqrt(sqrt(5)/8 + 5/8)/24 + 5^(7/10)*6^(4/5)*sqrt(5/8 - sqrt(5)/8)/24 + 5^(7/10)*6^(4/5)*sqrt(sqrt(5)/8 + 5/8)/24)^2 + (-5^(1/5)*6^(4/5)*sqrt(5/8 - sqrt(5)/8)*sqrt(sqrt(5)/8 + 5/8)/6 + 5^(1/5)*6^(4/5)/24)^2 + 2*i*(-5^(1/5)*6^(4/5)*sqrt(5/8 - sqrt(5)/8)*sqrt(sqrt(5)/8 + 5/8)/6 + 5^(1/5)*6^(4/5)/24)*(-5^(1/5)*6^(4/5)*sqrt(5/8 - sqrt(5)/8)/24 + 5^(1/5)*6^(4/5)*sqrt(sqrt(5)/8 + 5/8)/24 + 5^(7/10)*6^(4/5)*sqrt(5/8 - sqrt(5)/8)/24 + 5^(7/10)*6^(4/5)*sqrt(sqrt(5)/8 + 5/8)/24)

Respuesta numérica [src]

x1 = 0.287282959208145 - 0.884166034065898*i

x2 = 0.287282959208147 - 0.884166034065896*i

x3 = 0.287282959208145 - 0.884166034065898*i

x4 = 0.287282959208145 + 0.884166034065898*i

x5 = 0.287282959208144 - 0.884166034065895*i

x5 = 0.287282959208144 - 0.884166034065895*i

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6x^2*sqrt(x)+5=0 la ecuación

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