Произведение корней x^6=-(12-8*x)^3

Сумма и произведение корней

сумма

               /                        /    /    ___\\\               /    /    ___\\          /                      /    /    ___\\\               /    /    ___\\          /                      /    /    ___\\\               /    /    ___\\          /                        /    /    ___\\\               /    /    ___\\
               |      ___     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      /

$$\left(- 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 \sqrt{3}\right)\right) + \left(\left(-2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + 2 \sqrt{3}\right)\right) + \left(\left(\left(2 + 6\right) + \left(-2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right)\right) + \left(- 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right)\right)\right)$$

=

  /                        /    /    ___\\\     /                        /    /    ___\\\     /                      /    /    ___\\\     /                      /    /    ___\\\
  |      ___     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      //

$$i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 \sqrt{3}\right) + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + 2 \sqrt{3}\right) + i \left(- 2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right) + i \left(2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)$$

произведение

    /       /                        /    /    ___\\\               /    /    ___\\\ /       /                      /    /    ___\\\               /    /    ___\\\ /       /                      /    /    ___\\\               /    /    ___\\\ /       /                        /    /    ___\\\               /    /    ___\\\
    |       |      ___     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      //

$$2 \cdot 6 \left(-2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right) \left(- 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(2 \sqrt{3} + 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)}\right)\right) \left(-2 + 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} + 2 \sqrt{3}\right)\right) \left(- 2 \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 + i \left(- 2 \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(7 \sqrt{3} \right)}}{2} \right)} - 2 \sqrt{3}\right)\right)$$

=

1728

$$1728$$