x^3+(195,206*10125/(2*60*337,5^2)-337,5)*x^2-(195,206*67500/120)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Teorema de Cardano-Vieta
es ecuación cúbica reducida
p x 2 + q x + v + x 3 = 0 p x^{2} + q x + v + x^{3} = 0 p x 2 + q x + v + x 3 = 0 donde
p = b a p = \frac{b}{a} p = a b p = − 227714897 675000 p = - \frac{227714897}{675000} p = − 675000 227714897 q = c a q = \frac{c}{a} q = a c q = 0 q = 0 q = 0 v = d a v = \frac{d}{a} v = a d v = ( − 97603 ) 1125 2 ⋅ 500 v = \frac{\left(-97603\right) 1125}{2 \cdot 500} v = 2 ⋅ 500 ( − 97603 ) 1125 Fórmulas de Cardano-Vieta
x 1 + x 2 + x 3 = − p x_{1} + x_{2} + x_{3} = - p x 1 + x 2 + x 3 = − p x 1 x 2 + x 1 x 3 + x 2 x 3 = q x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q x 1 x 2 + x 1 x 3 + x 2 x 3 = q x 1 x 2 x 3 = v x_{1} x_{2} x_{3} = v x 1 x 2 x 3 = v x 1 + x 2 + x 3 = 227714897 675000 x_{1} + x_{2} + x_{3} = \frac{227714897}{675000} x 1 + x 2 + x 3 = 675000 227714897 x 1 x 2 + x 1 x 3 + x 2 x 3 = 0 x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0 x 1 x 2 + x 1 x 3 + x 2 x 3 = 0 x 1 x 2 x 3 = ( − 97603 ) 1125 2 ⋅ 500 x_{1} x_{2} x_{3} = \frac{\left(-97603\right) 1125}{2 \cdot 500} x 1 x 2 x 3 = 2 ⋅ 500 ( − 97603 ) 1125
__________________________________________________________________ / __________________________________________________________________ \
/ _________________________________ | / _________________________________ |
/ 12263835937251656146712273 \/ 5873695133855530253246383658095 | ___ / 12263835937251656146712273 \/ 5873695133855530253246383658095 |
3 / -------------------------- + ----------------------------------- | \/ 3 *3 / -------------------------- + ----------------------------------- ___ |
227714897 51854074315720609 \/ 8303765625000000000 6075000000 | \/ 8303765625000000000 6075000000 51854074315720609*\/ 3 |
x1 = --------- - ------------------------------------------------------------------------------------- - ----------------------------------------------------------------------- + I*|- ----------------------------------------------------------------------------- + -------------------------------------------------------------------------------------|
2025000 __________________________________________________________________ 2 | 2 __________________________________________________________________|
/ _________________________________ | / _________________________________ |
/ 12263835937251656146712273 \/ 5873695133855530253246383658095 | / 12263835937251656146712273 \/ 5873695133855530253246383658095 |
8201250000000*3 / -------------------------- + ----------------------------------- | 8201250000000*3 / -------------------------- + ----------------------------------- |
\/ 8303765625000000000 6075000000 \ \/ 8303765625000000000 6075000000 /
x 1 = − 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 − 51854074315720609 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 + 227714897 2025000 + i ( − 3 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 + 51854074315720609 3 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 ) x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} - \frac{51854074315720609}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} + \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}\right) x 1 = − 2 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 − 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 + 2025000 227714897 + i − 2 3 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 + 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 3
__________________________________________________________________ / __________________________________________________________________ \
/ _________________________________ | / _________________________________ |
/ 12263835937251656146712273 \/ 5873695133855530253246383658095 | ___ / 12263835937251656146712273 \/ 5873695133855530253246383658095 |
3 / -------------------------- + ----------------------------------- |\/ 3 *3 / -------------------------- + ----------------------------------- ___ |
227714897 51854074315720609 \/ 8303765625000000000 6075000000 | \/ 8303765625000000000 6075000000 51854074315720609*\/ 3 |
x2 = --------- - ------------------------------------------------------------------------------------- - ----------------------------------------------------------------------- + I*|----------------------------------------------------------------------------- - -------------------------------------------------------------------------------------|
2025000 __________________________________________________________________ 2 | 2 __________________________________________________________________|
/ _________________________________ | / _________________________________ |
/ 12263835937251656146712273 \/ 5873695133855530253246383658095 | / 12263835937251656146712273 \/ 5873695133855530253246383658095 |
8201250000000*3 / -------------------------- + ----------------------------------- | 8201250000000*3 / -------------------------- + ----------------------------------- |
\/ 8303765625000000000 6075000000 \ \/ 8303765625000000000 6075000000 /
x 2 = − 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 − 51854074315720609 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 + 227714897 2025000 + i ( − 51854074315720609 3 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 + 3 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 ) x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} - \frac{51854074315720609}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + i \left(- \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2}\right) x 2 = − 2 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 − 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 + 2025000 227714897 + i − 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 3 + 2 3 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273
__________________________________________________________________
/ _________________________________
227714897 / 12263835937251656146712273 \/ 5873695133855530253246383658095 51854074315720609
x3 = --------- + 3 / -------------------------- + ----------------------------------- + -------------------------------------------------------------------------------------
2025000 \/ 8303765625000000000 6075000000 __________________________________________________________________
/ _________________________________
/ 12263835937251656146712273 \/ 5873695133855530253246383658095
4100625000000*3 / -------------------------- + -----------------------------------
\/ 8303765625000000000 6075000000
x 3 = 51854074315720609 4100625000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 + 227714897 2025000 + 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 x_{3} = \frac{51854074315720609}{4100625000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}} x 3 = 4100625000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 + 2025000 227714897 + 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273
x3 = 51854074315720609/(4100625000000*(sqrt(5873695133855530253246383658095)/6075000000 + 12263835937251656146712273/8303765625000000000)^(1/3)) + 227714897/2025000 + (sqrt(5873695133855530253246383658095)/6075000000 + 12263835937251656146712273/8303765625000000000)^(1/3)
Suma y producto de raíces
[src]
__________________________________________________________________ / __________________________________________________________________ \ __________________________________________________________________ / __________________________________________________________________ \
/ _________________________________ | / _________________________________ | / _________________________________ | / _________________________________ |
/ 12263835937251656146712273 \/ 5873695133855530253246383658095 | ___ / 12263835937251656146712273 \/ 5873695133855530253246383658095 | / 12263835937251656146712273 \/ 5873695133855530253246383658095 | ___ / 12263835937251656146712273 \/ 5873695133855530253246383658095 | __________________________________________________________________
3 / -------------------------- + ----------------------------------- | \/ 3 *3 / -------------------------- + ----------------------------------- ___ | 3 / -------------------------- + ----------------------------------- |\/ 3 *3 / -------------------------- + ----------------------------------- ___ | / _________________________________
227714897 51854074315720609 \/ 8303765625000000000 6075000000 | \/ 8303765625000000000 6075000000 51854074315720609*\/ 3 | 227714897 51854074315720609 \/ 8303765625000000000 6075000000 | \/ 8303765625000000000 6075000000 51854074315720609*\/ 3 | 227714897 / 12263835937251656146712273 \/ 5873695133855530253246383658095 51854074315720609
--------- - ------------------------------------------------------------------------------------- - ----------------------------------------------------------------------- + I*|- ----------------------------------------------------------------------------- + -------------------------------------------------------------------------------------| + --------- - ------------------------------------------------------------------------------------- - ----------------------------------------------------------------------- + I*|----------------------------------------------------------------------------- - -------------------------------------------------------------------------------------| + --------- + 3 / -------------------------- + ----------------------------------- + -------------------------------------------------------------------------------------
2025000 __________________________________________________________________ 2 | 2 __________________________________________________________________| 2025000 __________________________________________________________________ 2 | 2 __________________________________________________________________| 2025000 \/ 8303765625000000000 6075000000 __________________________________________________________________
/ _________________________________ | / _________________________________ | / _________________________________ | / _________________________________ | / _________________________________
/ 12263835937251656146712273 \/ 5873695133855530253246383658095 | / 12263835937251656146712273 \/ 5873695133855530253246383658095 | / 12263835937251656146712273 \/ 5873695133855530253246383658095 | / 12263835937251656146712273 \/ 5873695133855530253246383658095 | / 12263835937251656146712273 \/ 5873695133855530253246383658095
8201250000000*3 / -------------------------- + ----------------------------------- | 8201250000000*3 / -------------------------- + ----------------------------------- | 8201250000000*3 / -------------------------- + ----------------------------------- | 8201250000000*3 / -------------------------- + ----------------------------------- | 4100625000000*3 / -------------------------- + -----------------------------------
\/ 8303765625000000000 6075000000 \ \/ 8303765625000000000 6075000000 / \/ 8303765625000000000 6075000000 \ \/ 8303765625000000000 6075000000 / \/ 8303765625000000000 6075000000
( 51854074315720609 4100625000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 + 227714897 2025000 + 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 ) + ( ( − 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 − 51854074315720609 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 + 227714897 2025000 + i ( − 3 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 + 51854074315720609 3 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 ) ) + ( − 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 − 51854074315720609 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 + 227714897 2025000 + i ( − 51854074315720609 3 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 + 3 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 ) ) ) \left(\frac{51854074315720609}{4100625000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} - \frac{51854074315720609}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} + \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} - \frac{51854074315720609}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + i \left(- \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2}\right)\right)\right) 4100625000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 + 2025000 227714897 + 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 + − 2 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 − 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 + 2025000 227714897 + i − 2 3 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 + 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 3 + − 2 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 − 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 + 2025000 227714897 + i − 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 3 + 2 3 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273
/ __________________________________________________________________ \ / __________________________________________________________________ \
| / _________________________________ | | / _________________________________ |
| ___ / 12263835937251656146712273 \/ 5873695133855530253246383658095 | | ___ / 12263835937251656146712273 \/ 5873695133855530253246383658095 |
|\/ 3 *3 / -------------------------- + ----------------------------------- ___ | | \/ 3 *3 / -------------------------- + ----------------------------------- ___ |
227714897 | \/ 8303765625000000000 6075000000 51854074315720609*\/ 3 | | \/ 8303765625000000000 6075000000 51854074315720609*\/ 3 |
--------- + I*|----------------------------------------------------------------------------- - -------------------------------------------------------------------------------------| + I*|- ----------------------------------------------------------------------------- + -------------------------------------------------------------------------------------|
675000 | 2 __________________________________________________________________| | 2 __________________________________________________________________|
| / _________________________________ | | / _________________________________ |
| / 12263835937251656146712273 \/ 5873695133855530253246383658095 | | / 12263835937251656146712273 \/ 5873695133855530253246383658095 |
| 8201250000000*3 / -------------------------- + ----------------------------------- | | 8201250000000*3 / -------------------------- + ----------------------------------- |
\ \/ 8303765625000000000 6075000000 / \ \/ 8303765625000000000 6075000000 /
227714897 675000 + i ( − 3 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 + 51854074315720609 3 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 ) + i ( − 51854074315720609 3 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 + 3 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 ) \frac{227714897}{675000} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} + \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}\right) + i \left(- \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2}\right) 675000 227714897 + i − 2 3 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 + 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 3 + i − 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 3 + 2 3 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273
/ __________________________________________________________________ / __________________________________________________________________ \\ / __________________________________________________________________ / __________________________________________________________________ \\
| / _________________________________ | / _________________________________ || | / _________________________________ | / _________________________________ ||
| / 12263835937251656146712273 \/ 5873695133855530253246383658095 | ___ / 12263835937251656146712273 \/ 5873695133855530253246383658095 || | / 12263835937251656146712273 \/ 5873695133855530253246383658095 | ___ / 12263835937251656146712273 \/ 5873695133855530253246383658095 || / __________________________________________________________________ \
| 3 / -------------------------- + ----------------------------------- | \/ 3 *3 / -------------------------- + ----------------------------------- ___ || | 3 / -------------------------- + ----------------------------------- |\/ 3 *3 / -------------------------- + ----------------------------------- ___ || | / _________________________________ |
|227714897 51854074315720609 \/ 8303765625000000000 6075000000 | \/ 8303765625000000000 6075000000 51854074315720609*\/ 3 || |227714897 51854074315720609 \/ 8303765625000000000 6075000000 | \/ 8303765625000000000 6075000000 51854074315720609*\/ 3 || |227714897 / 12263835937251656146712273 \/ 5873695133855530253246383658095 51854074315720609 |
|--------- - ------------------------------------------------------------------------------------- - ----------------------------------------------------------------------- + I*|- ----------------------------------------------------------------------------- + -------------------------------------------------------------------------------------||*|--------- - ------------------------------------------------------------------------------------- - ----------------------------------------------------------------------- + I*|----------------------------------------------------------------------------- - -------------------------------------------------------------------------------------||*|--------- + 3 / -------------------------- + ----------------------------------- + -------------------------------------------------------------------------------------|
| 2025000 __________________________________________________________________ 2 | 2 __________________________________________________________________|| | 2025000 __________________________________________________________________ 2 | 2 __________________________________________________________________|| | 2025000 \/ 8303765625000000000 6075000000 __________________________________________________________________|
| / _________________________________ | / _________________________________ || | / _________________________________ | / _________________________________ || | / _________________________________ |
| / 12263835937251656146712273 \/ 5873695133855530253246383658095 | / 12263835937251656146712273 \/ 5873695133855530253246383658095 || | / 12263835937251656146712273 \/ 5873695133855530253246383658095 | / 12263835937251656146712273 \/ 5873695133855530253246383658095 || | / 12263835937251656146712273 \/ 5873695133855530253246383658095 |
| 8201250000000*3 / -------------------------- + ----------------------------------- | 8201250000000*3 / -------------------------- + ----------------------------------- || | 8201250000000*3 / -------------------------- + ----------------------------------- | 8201250000000*3 / -------------------------- + ----------------------------------- || | 4100625000000*3 / -------------------------- + ----------------------------------- |
\ \/ 8303765625000000000 6075000000 \ \/ 8303765625000000000 6075000000 // \ \/ 8303765625000000000 6075000000 \ \/ 8303765625000000000 6075000000 // \ \/ 8303765625000000000 6075000000 /
( − 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 − 51854074315720609 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 + 227714897 2025000 + i ( − 51854074315720609 3 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 + 3 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 ) ) ( − 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 − 51854074315720609 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 + 227714897 2025000 + i ( − 3 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 2 + 51854074315720609 3 8201250000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 ) ) ( 51854074315720609 4100625000000 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 + 227714897 2025000 + 5873695133855530253246383658095 6075000000 + 12263835937251656146712273 8303765625000000000 3 ) \left(- \frac{\sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} - \frac{51854074315720609}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + i \left(- \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} - \frac{51854074315720609}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} + \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}\right)\right) \left(\frac{51854074315720609}{4100625000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}\right) − 2 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 − 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 + 2025000 227714897 + i − 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 3 + 2 3 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 − 2 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 − 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 + 2025000 227714897 + i − 2 3 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 + 8201250000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 3 4100625000000 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273 51854074315720609 + 2025000 227714897 + 3 6075000000 5873695133855530253246383658095 + 8303765625000000000 12263835937251656146712273
878427 8 \frac{878427}{8} 8 878427
x1 = -0.479671415379271 + 18.0091571499161*i
x3 = -0.479671415379271 - 18.0091571499161*i
x3 = -0.479671415379271 - 18.0091571499161*i