Произведение корней x^6=-(7*x+10)^3
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Решение
Сумма и произведение корней
[src]
сумма
/ / / ___\\\ / / ___\\ / / / ___\\\ / / ___\\ / / / ___\\\ / / ___\\ / / / ___\\\ / / ___\\
| | |89*\/ 3 ||| | |89*\/ 3 || | | |89*\/ 3 ||| | |89*\/ 3 || | | |89*\/ 3 ||| | |89*\/ 3 || | | |89*\/ 3 ||| | |89*\/ 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 /|
| ___ \/ 5961 *cos|--------------|| \/ 5961 *sin|--------------| | ___ \/ 5961 *cos|--------------|| \/ 5961 *sin|--------------| | ___ \/ 5961 *cos|--------------|| \/ 5961 *sin|--------------| | ___ \/ 5961 *cos|--------------|| \/ 5961 *sin|--------------|
7 | 7*\/ 3 \ 2 /| \ 2 / 7 |7*\/ 3 \ 2 /| \ 2 / 7 | 7*\/ 3 \ 2 /| \ 2 / 7 |7*\/ 3 \ 2 /| \ 2 /
-5 - 2 + - + I*|- ------- + ----------------------------| - ---------------------------- + - + I*|------- + ----------------------------| + ---------------------------- + - + I*|- ------- - ----------------------------| + ---------------------------- + - + I*|------- - ----------------------------| - ----------------------------
4 \ 4 2 / 2 4 \ 4 2 / 2 4 \ 4 2 / 2 4 \ 4 2 / 2
$$\left(- \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7}{4} + i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7 \sqrt{3}}{4}\right)\right) + \left(\left(\frac{7}{4} + \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{7 \sqrt{3}}{4}\right)\right) + \left(\left(\left(-5 - 2\right) + \left(- \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7}{4} + i \left(- \frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right)\right)\right) + \left(\frac{7}{4} + \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(\frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right)\right)\right)\right)$$
=
/ / / ___\\\ / / / ___\\\ / / / ___\\\ / / / ___\\\ | | |89*\/ 3 ||| | | |89*\/ 3 ||| | | |89*\/ 3 ||| | | |89*\/ 3 ||| | |atan|--------||| | |atan|--------||| | |atan|--------||| | |atan|--------||| | 4 ______ | \ 9 /|| | 4 ______ | \ 9 /|| | 4 ______ | \ 9 /|| | 4 ______ | \ 9 /|| | ___ \/ 5961 *cos|--------------|| | ___ \/ 5961 *cos|--------------|| | ___ \/ 5961 *cos|--------------|| | ___ \/ 5961 *cos|--------------|| | 7*\/ 3 \ 2 /| | 7*\/ 3 \ 2 /| |7*\/ 3 \ 2 /| |7*\/ 3 \ 2 /| I*|- ------- + ----------------------------| + I*|- ------- - ----------------------------| + I*|------- + ----------------------------| + I*|------- - ----------------------------| \ 4 2 / \ 4 2 / \ 4 2 / \ 4 2 /
$$i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{7 \sqrt{3}}{4}\right) + i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7 \sqrt{3}}{4}\right) + i \left(- \frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right) + i \left(\frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right)$$
произведение
/ / / / ___\\\ / / ___\\\ / / / / ___\\\ / / ___\\\ / / / / ___\\\ / / ___\\\ / / / / ___\\\ / / ___\\\
| | | |89*\/ 3 ||| | |89*\/ 3 ||| | | | |89*\/ 3 ||| | |89*\/ 3 ||| | | | |89*\/ 3 ||| | |89*\/ 3 ||| | | | |89*\/ 3 ||| | |89*\/ 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 /||
| | ___ \/ 5961 *cos|--------------|| \/ 5961 *sin|--------------|| | | ___ \/ 5961 *cos|--------------|| \/ 5961 *sin|--------------|| | | ___ \/ 5961 *cos|--------------|| \/ 5961 *sin|--------------|| | | ___ \/ 5961 *cos|--------------|| \/ 5961 *sin|--------------||
|7 | 7*\/ 3 \ 2 /| \ 2 /| |7 |7*\/ 3 \ 2 /| \ 2 /| |7 | 7*\/ 3 \ 2 /| \ 2 /| |7 |7*\/ 3 \ 2 /| \ 2 /|
-5*(-2)*|- + I*|- ------- + ----------------------------| - ----------------------------|*|- + I*|------- + ----------------------------| + ----------------------------|*|- + I*|- ------- - ----------------------------| + ----------------------------|*|- + I*|------- - ----------------------------| - ----------------------------|
\4 \ 4 2 / 2 / \4 \ 4 2 / 2 / \4 \ 4 2 / 2 / \4 \ 4 2 / 2 /
$$- -10 \left(- \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7}{4} + i \left(- \frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right)\right) \left(\frac{7}{4} + \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(\frac{7 \sqrt{3}}{4} + \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2}\right)\right) \left(\frac{7}{4} + \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} - \frac{7 \sqrt{3}}{4}\right)\right) \left(- \frac{\sqrt[4]{5961} \sin{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7}{4} + i \left(- \frac{\sqrt[4]{5961} \cos{\left(\frac{\operatorname{atan}{\left(\frac{89 \sqrt{3}}{9} \right)}}{2} \right)}}{2} + \frac{7 \sqrt{3}}{4}\right)\right)$$
=
1000
$$1000$$