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x⁶=(4x-3)³ la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
 6            3
x  = (4*x - 3)
x6=(4x−3)3x^{6} = \left(4 x - 3\right)^{3}
Simplificar
Gráfica
02468-8-6-4-21012-50000005000000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 1
x1=1x_{1} = 1 
x2 = 3
x2=3x_{2} = 3 
            /                    /    /    ___\\\             /    /    ___\\
            |    ___   4 ____    |atan\7*\/ 3 /||   4 ____    |atan\7*\/ 3 /|
x3 = -1 + I*|- \/ 3  + \/ 37 *cos|-------------|| + \/ 37 *sin|-------------|
            \                    \      2      //             \      2      /
x3=−1+374sin⁡(atan⁡(73)2)+i(−3+374cos⁡(atan⁡(73)2))x_{3} = -1 + \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- \sqrt{3} + \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right) 
            /                  /    /    ___\\\             /    /    ___\\
            |  ___   4 ____    |atan\7*\/ 3 /||   4 ____    |atan\7*\/ 3 /|
x4 = -1 + I*|\/ 3  + \/ 37 *cos|-------------|| - \/ 37 *sin|-------------|
            \                  \      2      //             \      2      /
x4=−374sin⁡(atan⁡(73)2)−1+i(3+374cos⁡(atan⁡(73)2))x_{4} = - \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 1 + i \left(\sqrt{3} + \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right) 
            /                  /    /    ___\\\             /    /    ___\\
            |  ___   4 ____    |atan\7*\/ 3 /||   4 ____    |atan\7*\/ 3 /|
x5 = -1 + I*|\/ 3  - \/ 37 *cos|-------------|| + \/ 37 *sin|-------------|
            \                  \      2      //             \      2      /
x5=−1+374sin⁡(atan⁡(73)2)+i(−374cos⁡(atan⁡(73)2)+3)x_{5} = -1 + \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + \sqrt{3}\right) 
            /                    /    /    ___\\\             /    /    ___\\
            |    ___   4 ____    |atan\7*\/ 3 /||   4 ____    |atan\7*\/ 3 /|
x6 = -1 + I*|- \/ 3  - \/ 37 *cos|-------------|| - \/ 37 *sin|-------------|
            \                    \      2      //             \      2      /
x6=−374sin⁡(atan⁡(73)2)−1+i(−374cos⁡(atan⁡(73)2)−3)x_{6} = - \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 1 + i \left(- \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - \sqrt{3}\right) 
x6 = -37^(1/4)*sin(atan(7*sqrt(3))/2) - 1 + i*(-37^(1/4)*cos(atan(7*sqrt(3))/2) - sqrt(3))
Suma y producto de raíces [src] 
suma
               /                    /    /    ___\\\             /    /    ___\\          /                  /    /    ___\\\             /    /    ___\\          /                  /    /    ___\\\             /    /    ___\\          /                    /    /    ___\\\             /    /    ___\\
               |    ___   4 ____    |atan\7*\/ 3 /||   4 ____    |atan\7*\/ 3 /|          |  ___   4 ____    |atan\7*\/ 3 /||   4 ____    |atan\7*\/ 3 /|          |  ___   4 ____    |atan\7*\/ 3 /||   4 ____    |atan\7*\/ 3 /|          |    ___   4 ____    |atan\7*\/ 3 /||   4 ____    |atan\7*\/ 3 /|
1 + 3 + -1 + I*|- \/ 3  + \/ 37 *cos|-------------|| + \/ 37 *sin|-------------| + -1 + I*|\/ 3  + \/ 37 *cos|-------------|| - \/ 37 *sin|-------------| + -1 + I*|\/ 3  - \/ 37 *cos|-------------|| + \/ 37 *sin|-------------| + -1 + I*|- \/ 3  - \/ 37 *cos|-------------|| - \/ 37 *sin|-------------|
               \                    \      2      //             \      2      /          \                  \      2      //             \      2      /          \                  \      2      //             \      2      /          \                    \      2      //             \      2      /
(−374sin⁡(atan⁡(73)2)−1+i(−374cos⁡(atan⁡(73)2)−3))+((−1+374sin⁡(atan⁡(73)2)+i(−374cos⁡(atan⁡(73)2)+3))+(((1+3)+(−1+374sin⁡(atan⁡(73)2)+i(−3+374cos⁡(atan⁡(73)2))))+(−374sin⁡(atan⁡(73)2)−1+i(3+374cos⁡(atan⁡(73)2)))))\left(- \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 1 + i \left(- \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - \sqrt{3}\right)\right) + \left(\left(-1 + \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + \sqrt{3}\right)\right) + \left(\left(\left(1 + 3\right) + \left(-1 + \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- \sqrt{3} + \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right)\right) + \left(- \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 1 + i \left(\sqrt{3} + \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right)\right)\right) 
=
  /                  /    /    ___\\\     /                  /    /    ___\\\     /                    /    /    ___\\\     /                    /    /    ___\\\
  |  ___   4 ____    |atan\7*\/ 3 /||     |  ___   4 ____    |atan\7*\/ 3 /||     |    ___   4 ____    |atan\7*\/ 3 /||     |    ___   4 ____    |atan\7*\/ 3 /||
I*|\/ 3  + \/ 37 *cos|-------------|| + I*|\/ 3  - \/ 37 *cos|-------------|| + I*|- \/ 3  + \/ 37 *cos|-------------|| + I*|- \/ 3  - \/ 37 *cos|-------------||
  \                  \      2      //     \                  \      2      //     \                    \      2      //     \                    \      2      //
i(−374cos⁡(atan⁡(73)2)−3)+i(−374cos⁡(atan⁡(73)2)+3)+i(−3+374cos⁡(atan⁡(73)2))+i(3+374cos⁡(atan⁡(73)2))i \left(- \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - \sqrt{3}\right) + i \left(- \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + \sqrt{3}\right) + i \left(- \sqrt{3} + \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right) + i \left(\sqrt{3} + \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right) 
producto
  /       /                    /    /    ___\\\             /    /    ___\\\ /       /                  /    /    ___\\\             /    /    ___\\\ /       /                  /    /    ___\\\             /    /    ___\\\ /       /                    /    /    ___\\\             /    /    ___\\\
  |       |    ___   4 ____    |atan\7*\/ 3 /||   4 ____    |atan\7*\/ 3 /|| |       |  ___   4 ____    |atan\7*\/ 3 /||   4 ____    |atan\7*\/ 3 /|| |       |  ___   4 ____    |atan\7*\/ 3 /||   4 ____    |atan\7*\/ 3 /|| |       |    ___   4 ____    |atan\7*\/ 3 /||   4 ____    |atan\7*\/ 3 /||
3*|-1 + I*|- \/ 3  + \/ 37 *cos|-------------|| + \/ 37 *sin|-------------||*|-1 + I*|\/ 3  + \/ 37 *cos|-------------|| - \/ 37 *sin|-------------||*|-1 + I*|\/ 3  - \/ 37 *cos|-------------|| + \/ 37 *sin|-------------||*|-1 + I*|- \/ 3  - \/ 37 *cos|-------------|| - \/ 37 *sin|-------------||
  \       \                    \      2      //             \      2      // \       \                  \      2      //             \      2      // \       \                  \      2      //             \      2      // \       \                    \      2      //             \      2      //
3(−1+374sin⁡(atan⁡(73)2)+i(−3+374cos⁡(atan⁡(73)2)))(−374sin⁡(atan⁡(73)2)−1+i(3+374cos⁡(atan⁡(73)2)))(−1+374sin⁡(atan⁡(73)2)+i(−374cos⁡(atan⁡(73)2)+3))(−374sin⁡(atan⁡(73)2)−1+i(−374cos⁡(atan⁡(73)2)−3))3 \left(-1 + \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- \sqrt{3} + \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right) \left(- \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 1 + i \left(\sqrt{3} + \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right) \left(-1 + \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + \sqrt{3}\right)\right) \left(- \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 1 + i \left(- \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - \sqrt{3}\right)\right) 
=
27
2727 
27
Respuesta numérica [src] 
x1 = 0.670742728593816 + 0.0821656252607644*i
x2 = 1.0
x3 = -2.67074272859382 + 3.54626724039852*i
x4 = 3.0
x5 = 0.670742728593816 - 0.0821656252607644*i
x6 = -2.67074272859382 - 3.54626724039852*i
x6 = -2.67074272859382 - 3.54626724039852*i
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