Произведение корней 3*x^2-32*sqrt(2*x)-22=0
Решение
Сумма и произведение корней
[src]
сумма
__________________________________________________________________________________________________________________________________________________________________________
/ __________________________
/ / _______
/ 176 / 2444480 4096*\/ 39526 3872 4096
/ --- - 2*3 / ------- + -------------- - ---------------------------------- + -----------------------------------------------------------------------------------------
_____________________________________________________________________________ / 9 \/ 729 243 __________________________ _____________________________________________________________________________
/ __________________________ / / _______ / __________________________
/ / _______ / / 2444480 4096*\/ 39526 / / _______
/ 88 / 2444480 4096*\/ 39526 3872 / 81*3 / ------- + -------------- / 88 / 2444480 4096*\/ 39526 3872
/ -- + 2*3 / ------- + -------------- + ---------------------------------- / \/ 729 243 9* / -- + 2*3 / ------- + -------------- + ----------------------------------
/ 9 \/ 729 243 __________________________ / / 9 \/ 729 243 __________________________
/ / _______ / / / _______
/ / 2444480 4096*\/ 39526 / / / 2444480 4096*\/ 39526
/ 81*3 / ------- + -------------- / / 81*3 / ------- + --------------
\/ \/ 729 243 \/ \/ \/ 729 243
--------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}} - \frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{176}{9} + \frac{4096}{9 \sqrt{\frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{88}{9} + 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}}}}}{2} + \frac{\sqrt{\frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{88}{9} + 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}}}{2}$$
=
__________________________________________________________________________________________________________________________________________________________________________
/ __________________________
/ / _______
/ 176 / 2444480 4096*\/ 39526 3872 4096
/ --- - 2*3 / ------- + -------------- - ---------------------------------- + -----------------------------------------------------------------------------------------
_____________________________________________________________________________ / 9 \/ 729 243 __________________________ _____________________________________________________________________________
/ __________________________ / / _______ / __________________________
/ / _______ / / 2444480 4096*\/ 39526 / / _______
/ 88 / 2444480 4096*\/ 39526 3872 / 81*3 / ------- + -------------- / 88 / 2444480 4096*\/ 39526 3872
/ -- + 2*3 / ------- + -------------- + ---------------------------------- / \/ 729 243 9* / -- + 2*3 / ------- + -------------- + ----------------------------------
/ 9 \/ 729 243 __________________________ / / 9 \/ 729 243 __________________________
/ / _______ / / / _______
/ / 2444480 4096*\/ 39526 / / / 2444480 4096*\/ 39526
/ 81*3 / ------- + -------------- / / 81*3 / ------- + --------------
\/ \/ 729 243 \/ \/ \/ 729 243
--------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}} - \frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{176}{9} + \frac{4096}{9 \sqrt{\frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{88}{9} + 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}}}}}{2} + \frac{\sqrt{\frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{88}{9} + 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}}}{2}$$
произведение
__________________________________________________________________________________________________________________________________________________________________________
/ __________________________
/ / _______
/ 176 / 2444480 4096*\/ 39526 3872 4096
/ --- - 2*3 / ------- + -------------- - ---------------------------------- + -----------------------------------------------------------------------------------------
_____________________________________________________________________________ / 9 \/ 729 243 __________________________ _____________________________________________________________________________
/ __________________________ / / _______ / __________________________
/ / _______ / / 2444480 4096*\/ 39526 / / _______
/ 88 / 2444480 4096*\/ 39526 3872 / 81*3 / ------- + -------------- / 88 / 2444480 4096*\/ 39526 3872
/ -- + 2*3 / ------- + -------------- + ---------------------------------- / \/ 729 243 9* / -- + 2*3 / ------- + -------------- + ----------------------------------
/ 9 \/ 729 243 __________________________ / / 9 \/ 729 243 __________________________
/ / _______ / / / _______
/ / 2444480 4096*\/ 39526 / / / 2444480 4096*\/ 39526
/ 81*3 / ------- + -------------- / / 81*3 / ------- + --------------
\/ \/ 729 243 \/ \/ \/ 729 243
--------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}} - \frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{176}{9} + \frac{4096}{9 \sqrt{\frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{88}{9} + 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}}}}}{2} + \frac{\sqrt{\frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{88}{9} + 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}}}{2}$$
=
/ _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________\
| 3/4 / ____________________________________________________________________ ____________________________________________________________________ |
|/ _______________________ / _______________________\\ / / _______________________ / _______________________\ _______________________ / _______________________ / _______________________\ _______________________ / _______________________\ |
___ || 3 / _______ | 3 / _______ || / / 3 / _______ | 3 / _______ | ___ / _______ / 3 / _______ | 3 / _______ | 3 / _______ | 3 / _______ | |
\/ 2 *\\121 + \/ 38195 + 192*\/ 39526 *\11 + \/ 38195 + 192*\/ 39526 // + \/ - 121*\/ 121 + \/ 38195 + 192*\/ 39526 *\11 + \/ 38195 + 192*\/ 39526 / + 384*\/ 2 *\/ 38195 + 192*\/ 39526 + \/ 121 + \/ 38195 + 192*\/ 39526 *\11 + \/ 38195 + 192*\/ 39526 / *\/ 38195 + 192*\/ 39526 *\22 - \/ 38195 + 192*\/ 39526 / /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
____________________________________________________________________
/ _______________________ / _______________________\ _______________________
4 / 3 / _______ | 3 / _______ | 6 / _______
3*\/ 121 + \/ 38195 + 192*\/ 39526 *\11 + \/ 38195 + 192*\/ 39526 / *\/ 38195 + 192*\/ 39526
$$\frac{\sqrt{2} \left(\sqrt{\left(22 - \sqrt[3]{192 \sqrt{39526} + 38195}\right) \sqrt{121 + \left(11 + \sqrt[3]{192 \sqrt{39526} + 38195}\right) \sqrt[3]{192 \sqrt{39526} + 38195}} \sqrt[3]{192 \sqrt{39526} + 38195} - 121 \sqrt{121 + \left(11 + \sqrt[3]{192 \sqrt{39526} + 38195}\right) \sqrt[3]{192 \sqrt{39526} + 38195}} + 384 \sqrt{2} \sqrt{192 \sqrt{39526} + 38195}} + \left(121 + \left(11 + \sqrt[3]{192 \sqrt{39526} + 38195}\right) \sqrt[3]{192 \sqrt{39526} + 38195}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{121 + \left(11 + \sqrt[3]{192 \sqrt{39526} + 38195}\right) \sqrt[3]{192 \sqrt{39526} + 38195}} \sqrt[6]{192 \sqrt{39526} + 38195}}$$