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6x^2*sqrt(x)+5=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
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
$$\cos{\left(\frac{5 p}{2} \right)} = -1$$
y
$$\sin{\left(\frac{5 p}{2} \right)} = 0$$
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:
$$x_{1} = \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6}\right)^{2}$$
$$x_{2} = \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} - \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}\right)^{2}$$
$$x_{3} = \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} - \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24}\right)^{2}$$
$$x_{4} = \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24}\right)^{2}$$
$$\sqrt{x} 6 x^{2} + 5 = 0$$
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
$$\cos{\left(\frac{5 p}{2} \right)} = -1$$
y
$$\sin{\left(\frac{5 p}{2} \right)} = 0$$
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:
$$x_{1} = \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6}\right)^{2}$$
$$x_{2} = \left(- \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} - \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}\right)^{2}$$
$$x_{3} = \left(\frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} - \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24}\right)^{2}$$
$$x_{4} = \left(- \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{6} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}}}{24} - \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{\sqrt[5]{5} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{24} + \frac{5^{\frac{7}{10}} \cdot 6^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{24}\right)^{2}$$
Suma y producto de raíces
[src]
suma
2 2 2 2 2
___________ / ___________ ___________\ / ___________ ___________\ / ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________\ / ___________ ___________ ___________ ___________\
/ ___\ / ___ /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(- \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)$$
=
2 2 2 2 2
/ ___________ ___________\ / ___________ ___________\ / ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________\ / ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________\ / ___________ ___________ ___________ ___________\ ___________
| / ___ / ___ | | / ___ / ___ | | / ___ / ___ | | / ___ / ___ / ___ / ___ | | / ___ / ___ / ___ / ___ | | / ___ / ___ | | / ___ / ___ | | / ___ / ___ / ___ / ___ | | / ___ / ___ | | / ___ / ___ / ___ / ___ | / ___\ / ___ /5 ___ 4/5 7/10 4/5\
2 2 | 5 ___ 4/5 / 5 \/ 5 / 5 \/ 5 | | 5 ___ 4/5 / 5 \/ 5 / 5 \/ 5 | | 5 ___ 4/5 / 5 \/ 5 7/10 4/5 / 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 ___ 4/5 / 5 \/ 5 7/10 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 | 2/5 3/5 |5 \/ 5 | 5 ___ 4/5 / 5 \/ 5 |\/ 5 *6 5 *6 |
/ 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
/ 2 \ / 2 2 \ / 2 2 \ / ___________ \ | / ___________ ___________\ / ___________ ___________\| |/ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________\ / ___________ ___________ ___________ ___________\| |/ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________\ / ___________ ___________ ___________ ___________\| | / ___\ / ___ /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