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x^6=-(12-8x)^3

x^6=-(12-8x)^3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
 6              3
x  = -(12 - 8*x)
x6=−(12−8x)3x^{6} = - \left(12 - 8 x\right)^{3}
Simplificar
Gráfica
-7.5-5.0-2.50.02.55.07.510.012.515.0-2000000020000000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
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 /|
2 + 6 + -2 + I*|- 2*\/ 3  + 2*\/ 37 *cos|-------------|| + 2*\/ 37 *sin|-------------| + -2 + I*|2*\/ 3  + 2*\/ 37 *cos|-------------|| - 2*\/ 37 *sin|-------------| + -2 + I*|2*\/ 3  - 2*\/ 37 *cos|-------------|| + 2*\/ 37 *sin|-------------| + -2 + I*|- 2*\/ 3  - 2*\/ 37 *cos|-------------|| - 2*\/ 37 *sin|-------------|
               \                        \      2      //               \      2      /          \                      \      2      //               \      2      /          \                      \      2      //               \      2      /          \                        \      2      //               \      2      /
(−2374sin⁡(atan⁡(73)2)−2+i(−2374cos⁡(atan⁡(73)2)−23))+((−2+2374sin⁡(atan⁡(73)2)+i(−2374cos⁡(atan⁡(73)2)+23))+(((2+6)+(−2+2374sin⁡(atan⁡(73)2)+i(−23+2374cos⁡(atan⁡(73)2))))+(−2374sin⁡(atan⁡(73)2)−2+i(23+2374cos⁡(atan⁡(73)2)))))\left(- 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 \sqrt{3}\right)\right) + \left(\left(-2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + 2 \sqrt{3}\right)\right) + \left(\left(\left(2 + 6\right) + \left(-2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right)\right) + \left(- 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(2 \sqrt{3} + 2 \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*|- 2*\/ 3  - 2*\/ 37 *cos|-------------|| + I*|- 2*\/ 3  + 2*\/ 37 *cos|-------------|| + I*|2*\/ 3  - 2*\/ 37 *cos|-------------|| + I*|2*\/ 3  + 2*\/ 37 *cos|-------------||
  \                        \      2      //     \                        \      2      //     \                      \      2      //     \                      \      2      //
i(−2374cos⁡(atan⁡(73)2)−23)+i(−2374cos⁡(atan⁡(73)2)+23)+i(−23+2374cos⁡(atan⁡(73)2))+i(23+2374cos⁡(atan⁡(73)2))i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 \sqrt{3}\right) + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + 2 \sqrt{3}\right) + i \left(- 2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right) + i \left(2 \sqrt{3} + 2 \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 /||
2*6*|-2 + I*|- 2*\/ 3  + 2*\/ 37 *cos|-------------|| + 2*\/ 37 *sin|-------------||*|-2 + I*|2*\/ 3  + 2*\/ 37 *cos|-------------|| - 2*\/ 37 *sin|-------------||*|-2 + I*|2*\/ 3  - 2*\/ 37 *cos|-------------|| + 2*\/ 37 *sin|-------------||*|-2 + I*|- 2*\/ 3  - 2*\/ 37 *cos|-------------|| - 2*\/ 37 *sin|-------------||
    \       \                        \      2      //               \      2      // \       \                      \      2      //               \      2      // \       \                      \      2      //               \      2      // \       \                        \      2      //               \      2      //
2⋅6(−2+2374sin⁡(atan⁡(73)2)+i(−23+2374cos⁡(atan⁡(73)2)))(−2374sin⁡(atan⁡(73)2)−2+i(23+2374cos⁡(atan⁡(73)2)))(−2+2374sin⁡(atan⁡(73)2)+i(−2374cos⁡(atan⁡(73)2)+23))(−2374sin⁡(atan⁡(73)2)−2+i(−2374cos⁡(atan⁡(73)2)−23))2 \cdot 6 \left(-2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right) \left(- 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right) \left(-2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + 2 \sqrt{3}\right)\right) \left(- 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 \sqrt{3}\right)\right) 
=
1728
17281728 
1728
Respuesta rápida [src] 
x1 = 2
x1=2x_{1} = 2 
x2 = 6
x2=6x_{2} = 6 
            /                        /    /    ___\\\               /    /    ___\\
            |      ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /|
x3 = -2 + I*|- 2*\/ 3  + 2*\/ 37 *cos|-------------|| + 2*\/ 37 *sin|-------------|
            \                        \      2      //               \      2      /
x3=−2+2374sin⁡(atan⁡(73)2)+i(−23+2374cos⁡(atan⁡(73)2))x_{3} = -2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt{3} + 2 \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 = -2 + I*|2*\/ 3  + 2*\/ 37 *cos|-------------|| - 2*\/ 37 *sin|-------------|
            \                      \      2      //               \      2      /
x4=−2374sin⁡(atan⁡(73)2)−2+i(23+2374cos⁡(atan⁡(73)2))x_{4} = - 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(2 \sqrt{3} + 2 \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 = -2 + I*|2*\/ 3  - 2*\/ 37 *cos|-------------|| + 2*\/ 37 *sin|-------------|
            \                      \      2      //               \      2      /
x5=−2+2374sin⁡(atan⁡(73)2)+i(−2374cos⁡(atan⁡(73)2)+23)x_{5} = -2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + 2 \sqrt{3}\right) 
            /                        /    /    ___\\\               /    /    ___\\
            |      ___     4 ____    |atan\7*\/ 3 /||     4 ____    |atan\7*\/ 3 /|
x6 = -2 + I*|- 2*\/ 3  - 2*\/ 37 *cos|-------------|| - 2*\/ 37 *sin|-------------|
            \                        \      2      //               \      2      /
x6=−2374sin⁡(atan⁡(73)2)−2+i(−2374cos⁡(atan⁡(73)2)−23)x_{6} = - 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 \sqrt{3}\right) 
x6 = -2*37^(1/4)*sin(atan(7*sqrt(3))/2) - 2 + i*(-2*37^(1/4)*cos(atan(7*sqrt(3))/2) - 2*sqrt(3))
Respuesta numérica [src] 
x1 = 2.0
x2 = 6.0
x3 = 1.34148545718763 + 0.164331250521529*i
x4 = 1.34148545718763 - 0.164331250521529*i
x5 = -5.34148545718763 + 7.09253448079704*i
x6 = -5.34148545718763 - 7.09253448079704*i
x6 = -5.34148545718763 - 7.09253448079704*i
Gráfico
x^6=-(12-8x)^3 la ecuación
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