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x^6=(5x-4)^3

x^6=(5x-4)^3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
 6            3
x  = (5*x - 4)
x6=(5x−4)3x^{6} = \left(5 x - 4\right)^{3}
Simplificar
Gráfica
02468-8-6-4-2141012-1000000010000000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
                /                        /    /     ___\\\               /    /     ___\\           /                      /    /     ___\\\               /    /     ___\\           /                      /    /     ___\\\               /    /     ___\\           /                        /    /     ___\\\               /    /     ___\\
                |                        |    |41*\/ 3 |||               |    |41*\/ 3 ||           |                      |    |41*\/ 3 |||               |    |41*\/ 3 ||           |                      |    |41*\/ 3 |||               |    |41*\/ 3 ||           |                        |    |41*\/ 3 |||               |    |41*\/ 3 ||
                |                        |atan|--------|||               |atan|--------||           |                      |atan|--------|||               |atan|--------||           |                      |atan|--------|||               |atan|--------||           |                        |atan|--------|||               |atan|--------||
                |            4 ______    |    \   9    /||   4 ______    |    \   9    /|           |          4 ______    |    \   9    /||   4 ______    |    \   9    /|           |          4 ______    |    \   9    /||   4 ______    |    \   9    /|           |            4 ______    |    \   9    /||   4 ______    |    \   9    /|
                |      ___   \/ 1281 *cos|--------------||   \/ 1281 *sin|--------------|           |    ___   \/ 1281 *cos|--------------||   \/ 1281 *sin|--------------|           |    ___   \/ 1281 *cos|--------------||   \/ 1281 *sin|--------------|           |      ___   \/ 1281 *cos|--------------||   \/ 1281 *sin|--------------|
          5     |  5*\/ 3                \      2       /|               \      2       /     5     |5*\/ 3                \      2       /|               \      2       /     5     |5*\/ 3                \      2       /|               \      2       /     5     |  5*\/ 3                \      2       /|               \      2       /
1 + 4 + - - + I*|- ------- + ----------------------------| + ---------------------------- + - - + I*|------- + ----------------------------| - ---------------------------- + - - + I*|------- - ----------------------------| + ---------------------------- + - - + I*|- ------- - ----------------------------| - ----------------------------
          4     \     4                   2              /                2                   4     \   4                   2              /                2                   4     \   4                   2              /                2                   4     \     4                   2              /                2
(−12814sin⁡(atan⁡(4139)2)2−54+i(−12814cos⁡(atan⁡(4139)2)2−534))+((−54+12814sin⁡(atan⁡(4139)2)2+i(−12814cos⁡(atan⁡(4139)2)2+534))+(((1+4)+(−54+12814sin⁡(atan⁡(4139)2)2+i(−534+12814cos⁡(atan⁡(4139)2)2)))+(−12814sin⁡(atan⁡(4139)2)2−54+i(534+12814cos⁡(atan⁡(4139)2)2))))\left(- \frac{\sqrt[4]{1281} \sin{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{5}{4} + i \left(- \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{5 \sqrt{3}}{4}\right)\right) + \left(\left(- \frac{5}{4} + \frac{\sqrt[4]{1281} \sin{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{5 \sqrt{3}}{4}\right)\right) + \left(\left(\left(1 + 4\right) + \left(- \frac{5}{4} + \frac{\sqrt[4]{1281} \sin{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(- \frac{5 \sqrt{3}}{4} + \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right)\right)\right) + \left(- \frac{\sqrt[4]{1281} \sin{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{5}{4} + i \left(\frac{5 \sqrt{3}}{4} + \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right)\right)\right)\right) 
=
  /                        /    /     ___\\\     /                        /    /     ___\\\     /                      /    /     ___\\\     /                      /    /     ___\\\
  |                        |    |41*\/ 3 |||     |                        |    |41*\/ 3 |||     |                      |    |41*\/ 3 |||     |                      |    |41*\/ 3 |||
  |                        |atan|--------|||     |                        |atan|--------|||     |                      |atan|--------|||     |                      |atan|--------|||
  |            4 ______    |    \   9    /||     |            4 ______    |    \   9    /||     |          4 ______    |    \   9    /||     |          4 ______    |    \   9    /||
  |      ___   \/ 1281 *cos|--------------||     |      ___   \/ 1281 *cos|--------------||     |    ___   \/ 1281 *cos|--------------||     |    ___   \/ 1281 *cos|--------------||
  |  5*\/ 3                \      2       /|     |  5*\/ 3                \      2       /|     |5*\/ 3                \      2       /|     |5*\/ 3                \      2       /|
I*|- ------- + ----------------------------| + I*|- ------- - ----------------------------| + I*|------- + ----------------------------| + I*|------- - ----------------------------|
  \     4                   2              /     \     4                   2              /     \   4                   2              /     \   4                   2              /
i(−12814cos⁡(atan⁡(4139)2)2−534)+i(−12814cos⁡(atan⁡(4139)2)2+534)+i(−534+12814cos⁡(atan⁡(4139)2)2)+i(534+12814cos⁡(atan⁡(4139)2)2)i \left(- \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{5 \sqrt{3}}{4}\right) + i \left(- \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{5 \sqrt{3}}{4}\right) + i \left(- \frac{5 \sqrt{3}}{4} + \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right) + i \left(\frac{5 \sqrt{3}}{4} + \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right) 
producto
  /        /                        /    /     ___\\\               /    /     ___\\\ /        /                      /    /     ___\\\               /    /     ___\\\ /        /                      /    /     ___\\\               /    /     ___\\\ /        /                        /    /     ___\\\               /    /     ___\\\
  |        |                        |    |41*\/ 3 |||               |    |41*\/ 3 ||| |        |                      |    |41*\/ 3 |||               |    |41*\/ 3 ||| |        |                      |    |41*\/ 3 |||               |    |41*\/ 3 ||| |        |                        |    |41*\/ 3 |||               |    |41*\/ 3 |||
  |        |                        |atan|--------|||               |atan|--------||| |        |                      |atan|--------|||               |atan|--------||| |        |                      |atan|--------|||               |atan|--------||| |        |                        |atan|--------|||               |atan|--------|||
  |        |            4 ______    |    \   9    /||   4 ______    |    \   9    /|| |        |          4 ______    |    \   9    /||   4 ______    |    \   9    /|| |        |          4 ______    |    \   9    /||   4 ______    |    \   9    /|| |        |            4 ______    |    \   9    /||   4 ______    |    \   9    /||
  |        |      ___   \/ 1281 *cos|--------------||   \/ 1281 *sin|--------------|| |        |    ___   \/ 1281 *cos|--------------||   \/ 1281 *sin|--------------|| |        |    ___   \/ 1281 *cos|--------------||   \/ 1281 *sin|--------------|| |        |      ___   \/ 1281 *cos|--------------||   \/ 1281 *sin|--------------||
  |  5     |  5*\/ 3                \      2       /|               \      2       /| |  5     |5*\/ 3                \      2       /|               \      2       /| |  5     |5*\/ 3                \      2       /|               \      2       /| |  5     |  5*\/ 3                \      2       /|               \      2       /|
4*|- - + I*|- ------- + ----------------------------| + ----------------------------|*|- - + I*|------- + ----------------------------| - ----------------------------|*|- - + I*|------- - ----------------------------| + ----------------------------|*|- - + I*|- ------- - ----------------------------| - ----------------------------|
  \  4     \     4                   2              /                2              / \  4     \   4                   2              /                2              / \  4     \   4                   2              /                2              / \  4     \     4                   2              /                2              /
4(−54+12814sin⁡(atan⁡(4139)2)2+i(−534+12814cos⁡(atan⁡(4139)2)2))(−12814sin⁡(atan⁡(4139)2)2−54+i(534+12814cos⁡(atan⁡(4139)2)2))(−54+12814sin⁡(atan⁡(4139)2)2+i(−12814cos⁡(atan⁡(4139)2)2+534))(−12814sin⁡(atan⁡(4139)2)2−54+i(−12814cos⁡(atan⁡(4139)2)2−534))4 \left(- \frac{5}{4} + \frac{\sqrt[4]{1281} \sin{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(- \frac{5 \sqrt{3}}{4} + \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right)\right) \left(- \frac{\sqrt[4]{1281} \sin{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{5}{4} + i \left(\frac{5 \sqrt{3}}{4} + \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right)\right) \left(- \frac{5}{4} + \frac{\sqrt[4]{1281} \sin{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{5 \sqrt{3}}{4}\right)\right) \left(- \frac{\sqrt[4]{1281} \sin{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{5}{4} + i \left(- \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{5 \sqrt{3}}{4}\right)\right) 
=
64
6464 
64
Respuesta rápida [src] 
x1 = 1
x1=1x_{1} = 1 
x2 = 4
x2=4x_{2} = 4 
             /                        /    /     ___\\\               /    /     ___\\
             |                        |    |41*\/ 3 |||               |    |41*\/ 3 ||
             |                        |atan|--------|||               |atan|--------||
             |            4 ______    |    \   9    /||   4 ______    |    \   9    /|
             |      ___   \/ 1281 *cos|--------------||   \/ 1281 *sin|--------------|
       5     |  5*\/ 3                \      2       /|               \      2       /
x3 = - - + I*|- ------- + ----------------------------| + ----------------------------
       4     \     4                   2              /                2
x3=−54+12814sin⁡(atan⁡(4139)2)2+i(−534+12814cos⁡(atan⁡(4139)2)2)x_{3} = - \frac{5}{4} + \frac{\sqrt[4]{1281} \sin{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(- \frac{5 \sqrt{3}}{4} + \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right) 
             /                      /    /     ___\\\               /    /     ___\\
             |                      |    |41*\/ 3 |||               |    |41*\/ 3 ||
             |                      |atan|--------|||               |atan|--------||
             |          4 ______    |    \   9    /||   4 ______    |    \   9    /|
             |    ___   \/ 1281 *cos|--------------||   \/ 1281 *sin|--------------|
       5     |5*\/ 3                \      2       /|               \      2       /
x4 = - - + I*|------- + ----------------------------| - ----------------------------
       4     \   4                   2              /                2
x4=−12814sin⁡(atan⁡(4139)2)2−54+i(534+12814cos⁡(atan⁡(4139)2)2)x_{4} = - \frac{\sqrt[4]{1281} \sin{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{5}{4} + i \left(\frac{5 \sqrt{3}}{4} + \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right) 
             /                      /    /     ___\\\               /    /     ___\\
             |                      |    |41*\/ 3 |||               |    |41*\/ 3 ||
             |                      |atan|--------|||               |atan|--------||
             |          4 ______    |    \   9    /||   4 ______    |    \   9    /|
             |    ___   \/ 1281 *cos|--------------||   \/ 1281 *sin|--------------|
       5     |5*\/ 3                \      2       /|               \      2       /
x5 = - - + I*|------- - ----------------------------| + ----------------------------
       4     \   4                   2              /                2
x5=−54+12814sin⁡(atan⁡(4139)2)2+i(−12814cos⁡(atan⁡(4139)2)2+534)x_{5} = - \frac{5}{4} + \frac{\sqrt[4]{1281} \sin{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{5 \sqrt{3}}{4}\right) 
             /                        /    /     ___\\\               /    /     ___\\
             |                        |    |41*\/ 3 |||               |    |41*\/ 3 ||
             |                        |atan|--------|||               |atan|--------||
             |            4 ______    |    \   9    /||   4 ______    |    \   9    /|
             |      ___   \/ 1281 *cos|--------------||   \/ 1281 *sin|--------------|
       5     |  5*\/ 3                \      2       /|               \      2       /
x6 = - - + I*|- ------- - ----------------------------| - ----------------------------
       4     \     4                   2              /                2
x6=−12814sin⁡(atan⁡(4139)2)2−54+i(−12814cos⁡(atan⁡(4139)2)2−534)x_{6} = - \frac{\sqrt[4]{1281} \sin{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{5}{4} + i \left(- \frac{\sqrt[4]{1281} \cos{\left(\frac{\operatorname{atan}{\left(\frac{41 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{5 \sqrt{3}}{4}\right) 
x6 = -1281^(1/4)*sin(atan(41*sqrt(3)/9)/2)/2 - 5/4 + i*(-1281^(1/4)*cos(atan(41*sqrt(3)/9)/2)/2 - 5*sqrt(3)/4)
Respuesta numérica [src] 
x1 = 1.0
x2 = -3.22772155321302 - 4.40925212498416*i
x3 = 0.72772155321302 - 0.0791251060619659*i
x4 = -3.22772155321302 + 4.40925212498416*i
x5 = 0.72772155321302 + 0.0791251060619659*i
x6 = 4.0
x6 = 4.0
Gráfico
x^6=(5x-4)^3 la ecuación
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