Произведение корней x^6=(3*x-2)^3
Решение
Сумма и произведение корней
[src]
сумма
/ / / ___\\\ / / ___\\ / / / ___\\\ / / ___\\ / / / ___\\\ / / ___\\ / / / ___\\\ / / ___\\
| 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /| | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /| | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /| | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /|
| ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------| | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------| | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------| | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------|
3 | 3*\/ 3 \ 2 /| \ 2 / 3 |3*\/ 3 \ 2 /| \ 2 / 3 |3*\/ 3 \ 2 /| \ 2 / 3 | 3*\/ 3 \ 2 /| \ 2 /
1 + 2 + - - + I*|- ------- + ---------------------------| + --------------------------- + - - + I*|------- + ---------------------------| - --------------------------- + - - + I*|------- - ---------------------------| + --------------------------- + - - + I*|- ------- - ---------------------------| - ---------------------------
4 \ 4 2 / 2 4 \ 4 2 / 2 4 \ 4 2 / 2 4 \ 4 2 / 2
$$\left(- \frac{\sqrt[4]{217} \sin{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} - \frac{3}{4} + i \left(- \frac{\sqrt[4]{217} \cos{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} - \frac{3 \sqrt{3}}{4}\right)\right) + \left(\left(- \frac{3}{4} + \frac{\sqrt[4]{217} \sin{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{217} \cos{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} + \frac{3 \sqrt{3}}{4}\right)\right) + \left(\left(\left(1 + 2\right) + \left(- \frac{3}{4} + \frac{\sqrt[4]{217} \sin{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} + i \left(- \frac{3 \sqrt{3}}{4} + \frac{\sqrt[4]{217} \cos{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2}\right)\right)\right) + \left(- \frac{\sqrt[4]{217} \sin{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} - \frac{3}{4} + i \left(\frac{3 \sqrt{3}}{4} + \frac{\sqrt[4]{217} \cos{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2}\right)\right)\right)\right)$$
=
/ / / ___\\\ / / / ___\\\ / / / ___\\\ / / / ___\\\ | 4 _____ |atan\17*\/ 3 /|| | 4 _____ |atan\17*\/ 3 /|| | 4 _____ |atan\17*\/ 3 /|| | 4 _____ |atan\17*\/ 3 /|| | ___ \/ 217 *cos|--------------|| | ___ \/ 217 *cos|--------------|| | ___ \/ 217 *cos|--------------|| | ___ \/ 217 *cos|--------------|| | 3*\/ 3 \ 2 /| | 3*\/ 3 \ 2 /| |3*\/ 3 \ 2 /| |3*\/ 3 \ 2 /| I*|- ------- + ---------------------------| + I*|- ------- - ---------------------------| + I*|------- + ---------------------------| + I*|------- - ---------------------------| \ 4 2 / \ 4 2 / \ 4 2 / \ 4 2 /
$$i \left(- \frac{\sqrt[4]{217} \cos{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} - \frac{3 \sqrt{3}}{4}\right) + i \left(- \frac{\sqrt[4]{217} \cos{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} + \frac{3 \sqrt{3}}{4}\right) + i \left(- \frac{3 \sqrt{3}}{4} + \frac{\sqrt[4]{217} \cos{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2}\right) + i \left(\frac{3 \sqrt{3}}{4} + \frac{\sqrt[4]{217} \cos{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2}\right)$$
произведение
/ / / / ___\\\ / / ___\\\ / / / / ___\\\ / / ___\\\ / / / / ___\\\ / / ___\\\ / / / / ___\\\ / / ___\\\ | | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /|| | | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /|| | | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /|| | | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /|| | | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------|| | | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------|| | | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------|| | | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------|| | 3 | 3*\/ 3 \ 2 /| \ 2 /| | 3 |3*\/ 3 \ 2 /| \ 2 /| | 3 |3*\/ 3 \ 2 /| \ 2 /| | 3 | 3*\/ 3 \ 2 /| \ 2 /| 2*|- - + I*|- ------- + ---------------------------| + ---------------------------|*|- - + I*|------- + ---------------------------| - ---------------------------|*|- - + I*|------- - ---------------------------| + ---------------------------|*|- - + I*|- ------- - ---------------------------| - ---------------------------| \ 4 \ 4 2 / 2 / \ 4 \ 4 2 / 2 / \ 4 \ 4 2 / 2 / \ 4 \ 4 2 / 2 /
$$2 \left(- \frac{3}{4} + \frac{\sqrt[4]{217} \sin{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} + i \left(- \frac{3 \sqrt{3}}{4} + \frac{\sqrt[4]{217} \cos{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2}\right)\right) \left(- \frac{\sqrt[4]{217} \sin{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} - \frac{3}{4} + i \left(\frac{3 \sqrt{3}}{4} + \frac{\sqrt[4]{217} \cos{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2}\right)\right) \left(- \frac{3}{4} + \frac{\sqrt[4]{217} \sin{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{217} \cos{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} + \frac{3 \sqrt{3}}{4}\right)\right) \left(- \frac{\sqrt[4]{217} \sin{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} - \frac{3}{4} + i \left(- \frac{\sqrt[4]{217} \cos{\left(\frac{\operatorname{atan}{\left(17 \sqrt{3} \right)}}{2} \right)}}{2} - \frac{3 \sqrt{3}}{4}\right)\right)$$
=
8
$$8$$