Сумма корней 6*40184897/(100*(x^3))+17799099/(1000*(x^2))=891*10^6
Решение
Сумма и произведение корней
[src]
сумма
_____________________________________________________ / _____________________________________________________ \ _____________________________________________________ / _____________________________________________________ \
/ ___________________________________ | / ___________________________________ | / ___________________________________ | / ___________________________________ |
/ 40184897 \/ 142442181927182540809472643836930 | ___ / 40184897 \/ 142442181927182540809472643836930 | / 40184897 \/ 142442181927182540809472643836930 | ___ / 40184897 \/ 142442181927182540809472643836930 | _____________________________________________________
3 / ----------- + ------------------------------------- | \/ 3 *3 / ----------- + ------------------------------------- ___ | 3 / ----------- + ------------------------------------- |\/ 3 *3 / ----------- + ------------------------------------- ___ | / ___________________________________
5933033 \/ 29700000000 8820900000000000000 | \/ 29700000000 8820900000000000000 5933033*\/ 3 | 5933033 \/ 29700000000 8820900000000000000 | \/ 29700000000 8820900000000000000 5933033*\/ 3 | / 40184897 \/ 142442181927182540809472643836930 5933033
- ------------------------------------------------------------------------ - ---------------------------------------------------------- + I*|- ---------------------------------------------------------------- + ------------------------------------------------------------------------| + - ------------------------------------------------------------------------ - ---------------------------------------------------------- + I*|---------------------------------------------------------------- - ------------------------------------------------------------------------| + 3 / ----------- + ------------------------------------- + -----------------------------------------------------------------------
_____________________________________________________ 2 | 2 _____________________________________________________| _____________________________________________________ 2 | 2 _____________________________________________________| \/ 29700000000 8820900000000000000 _____________________________________________________
/ ___________________________________ | / ___________________________________ | / ___________________________________ | / ___________________________________ | / ___________________________________
/ 40184897 \/ 142442181927182540809472643836930 | / 40184897 \/ 142442181927182540809472643836930 | / 40184897 \/ 142442181927182540809472643836930 | / 40184897 \/ 142442181927182540809472643836930 | / 40184897 \/ 142442181927182540809472643836930
1782000000000*3 / ----------- + ------------------------------------- | 1782000000000*3 / ----------- + ------------------------------------- | 1782000000000*3 / ----------- + ------------------------------------- | 1782000000000*3 / ----------- + ------------------------------------- | 891000000000*3 / ----------- + -------------------------------------
\/ 29700000000 8820900000000000000 \ \/ 29700000000 8820900000000000000 / \/ 29700000000 8820900000000000000 \ \/ 29700000000 8820900000000000000 / \/ 29700000000 8820900000000000000
$$\left(\frac{5933033}{891000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} - \frac{5933033}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} + \frac{5933033 \sqrt{3}}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} - \frac{5933033}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + i \left(- \frac{5933033 \sqrt{3}}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2}\right)\right)\right)$$
=
/ _____________________________________________________ \ / _____________________________________________________ \ | / ___________________________________ | | / ___________________________________ | | ___ / 40184897 \/ 142442181927182540809472643836930 | | ___ / 40184897 \/ 142442181927182540809472643836930 | |\/ 3 *3 / ----------- + ------------------------------------- ___ | | \/ 3 *3 / ----------- + ------------------------------------- ___ | | \/ 29700000000 8820900000000000000 5933033*\/ 3 | | \/ 29700000000 8820900000000000000 5933033*\/ 3 | I*|---------------------------------------------------------------- - ------------------------------------------------------------------------| + I*|- ---------------------------------------------------------------- + ------------------------------------------------------------------------| | 2 _____________________________________________________| | 2 _____________________________________________________| | / ___________________________________ | | / ___________________________________ | | / 40184897 \/ 142442181927182540809472643836930 | | / 40184897 \/ 142442181927182540809472643836930 | | 1782000000000*3 / ----------- + ------------------------------------- | | 1782000000000*3 / ----------- + ------------------------------------- | \ \/ 29700000000 8820900000000000000 / \ \/ 29700000000 8820900000000000000 /
$$i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} + \frac{5933033 \sqrt{3}}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}\right) + i \left(- \frac{5933033 \sqrt{3}}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2}\right)$$
произведение
/ _____________________________________________________ / _____________________________________________________ \\ / _____________________________________________________ / _____________________________________________________ \\ | / ___________________________________ | / ___________________________________ || | / ___________________________________ | / ___________________________________ || | / 40184897 \/ 142442181927182540809472643836930 | ___ / 40184897 \/ 142442181927182540809472643836930 || | / 40184897 \/ 142442181927182540809472643836930 | ___ / 40184897 \/ 142442181927182540809472643836930 || / _____________________________________________________ \ | 3 / ----------- + ------------------------------------- | \/ 3 *3 / ----------- + ------------------------------------- ___ || | 3 / ----------- + ------------------------------------- |\/ 3 *3 / ----------- + ------------------------------------- ___ || | / ___________________________________ | | 5933033 \/ 29700000000 8820900000000000000 | \/ 29700000000 8820900000000000000 5933033*\/ 3 || | 5933033 \/ 29700000000 8820900000000000000 | \/ 29700000000 8820900000000000000 5933033*\/ 3 || | / 40184897 \/ 142442181927182540809472643836930 5933033 | |- ------------------------------------------------------------------------ - ---------------------------------------------------------- + I*|- ---------------------------------------------------------------- + ------------------------------------------------------------------------||*|- ------------------------------------------------------------------------ - ---------------------------------------------------------- + I*|---------------------------------------------------------------- - ------------------------------------------------------------------------||*|3 / ----------- + ------------------------------------- + -----------------------------------------------------------------------| | _____________________________________________________ 2 | 2 _____________________________________________________|| | _____________________________________________________ 2 | 2 _____________________________________________________|| |\/ 29700000000 8820900000000000000 _____________________________________________________| | / ___________________________________ | / ___________________________________ || | / ___________________________________ | / ___________________________________ || | / ___________________________________ | | / 40184897 \/ 142442181927182540809472643836930 | / 40184897 \/ 142442181927182540809472643836930 || | / 40184897 \/ 142442181927182540809472643836930 | / 40184897 \/ 142442181927182540809472643836930 || | / 40184897 \/ 142442181927182540809472643836930 | | 1782000000000*3 / ----------- + ------------------------------------- | 1782000000000*3 / ----------- + ------------------------------------- || | 1782000000000*3 / ----------- + ------------------------------------- | 1782000000000*3 / ----------- + ------------------------------------- || | 891000000000*3 / ----------- + ------------------------------------- | \ \/ 29700000000 8820900000000000000 \ \/ 29700000000 8820900000000000000 // \ \/ 29700000000 8820900000000000000 \ \/ 29700000000 8820900000000000000 // \ \/ 29700000000 8820900000000000000 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} - \frac{5933033}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + i \left(- \frac{5933033 \sqrt{3}}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} - \frac{5933033}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} + \frac{5933033 \sqrt{3}}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}\right)\right) \left(\frac{5933033}{891000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}\right)$$
=
40184897 ----------- 14850000000
$$\frac{40184897}{14850000000}$$