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(15376.0*t-388.0)*(-70.0*t+(-62.0*t+1.0)^2+8.0)+(19600.0*t-404.0)*(-62.0*t+(-70.0*t+1.0)^2+12.0)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                /                   2    \                   /                   2     \    
(15376*t - 388)*\-70*t + (-62*t + 1)  + 8/ + (19600*t - 404)*\-62*t + (-70*t + 1)  + 12/ = 0
(15376t−388)((−70t+(1−62t)2)+8)+(19600t−404)((−62t+(1−70t)2)+12)=0\left(15376 t - 388\right) \left(\left(- 70 t + \left(1 - 62 t\right)^{2}\right) + 8\right) + \left(19600 t - 404\right) \left(\left(- 62 t + \left(1 - 70 t\right)^{2}\right) + 12\right) = 0
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Suma y producto de raíces [src] 
suma
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                                                                                        /    217400660807751      3*\/ 226481291323535624673       |  ___    /    217400660807751      3*\/ 226481291323535624673                                                                             |                                                                                           /    217400660807751      3*\/ 226481291323535624673       |                                                                               ___    /    217400660807751      3*\/ 226481291323535624673  |                /    217400660807751      3*\/ 226481291323535624673                                                                             
                                                                                     3 /   -------------------- + ---------------------------      |\/ 3 *3 /   -------------------- + ---------------------------                                             ___                            |                                                                                        3 /   -------------------- + ---------------------------      |                                           ___                               \/ 3 *3 /   -------------------- + --------------------------- |             3 /   -------------------- + ---------------------------                                                                            
 108471                                 48041841811                                  \/    28490909537802128272          94023741269056            |      \/    28490909537802128272          94023741269056                                     48041841811*\/ 3                             |    108471                                 48041841811                                  \/    28490909537802128272          94023741269056            |                             48041841811*\/ 3                                      \/    28490909537802128272          94023741269056       |    108471   \/    28490909537802128272          94023741269056                                        48041841811                               
------- - ------------------------------------------------------------------------ + --------------------------------------------------------- + I*|--------------------------------------------------------------- + ------------------------------------------------------------------------| + ------- - ------------------------------------------------------------------------ + --------------------------------------------------------- + I*|- ------------------------------------------------------------------------ - ---------------------------------------------------------------| + ------- - --------------------------------------------------------- + ------------------------------------------------------------------------
4848292                       ____________________________________________________                               6                                 |                               6                                                      ____________________________________________________|   4848292                       ____________________________________________________                               6                                 |                      ____________________________________________________                                  6                               |   4848292                               3                                                   ____________________________________________________
                             /                            _______________________                                                                  |                                                                                     /                            _______________________ |                                /                            _______________________                                                                  |                     /                            _______________________                                                                   |                                                                                            /                            _______________________ 
                            /    217400660807751      3*\/ 226481291323535624673                                                                   |                                                                                    /    217400660807751      3*\/ 226481291323535624673  |                               /    217400660807751      3*\/ 226481291323535624673                                                                   |                    /    217400660807751      3*\/ 226481291323535624673                                                                    |                                                                                           /    217400660807751      3*\/ 226481291323535624673  
          47011870634528*3 /   -------------------- + ---------------------------                                                                  |                                                                  47011870634528*3 /   -------------------- + --------------------------- |             47011870634528*3 /   -------------------- + ---------------------------                                                                  |  47011870634528*3 /   -------------------- + ---------------------------                                                                   |                                                                         23505935317264*3 /   -------------------- + --------------------------- 
                         \/    28490909537802128272          94023741269056                                                                        \                                                                                 \/    28490909537802128272          94023741269056       /                            \/    28490909537802128272          94023741269056                                                                        \                 \/    28490909537802128272          94023741269056                                                                         /                                                                                        \/    28490909537802128272          94023741269056
(−21740066080775128490909537802128272+32264812913235356246739402374126905633+1084714848292+480418418112350593531726421740066080775128490909537802128272+3226481291323535624673940237412690563)+((−480418418114701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563+21740066080775128490909537802128272+32264812913235356246739402374126905636+1084714848292+i(−321740066080775128490909537802128272+32264812913235356246739402374126905636−4804184181134701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563))+(−480418418114701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563+21740066080775128490909537802128272+32264812913235356246739402374126905636+1084714848292+i(4804184181134701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563+321740066080775128490909537802128272+32264812913235356246739402374126905636)))\left(- \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{3} + \frac{108471}{4848292} + \frac{48041841811}{23505935317264 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}\right) + \left(\left(- \frac{48041841811}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} + \frac{108471}{4848292} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} - \frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}\right)\right) + \left(- \frac{48041841811}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} + \frac{108471}{4848292} + i \left(\frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6}\right)\right)\right) 
=
            /                                                                                        ____________________________________________________\     /           ____________________________________________________                                                                           \
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            |                                                                               ___    /    217400660807751      3*\/ 226481291323535624673  |     |  ___    /    217400660807751      3*\/ 226481291323535624673                                                                             |
            |                                           ___                               \/ 3 *3 /   -------------------- + --------------------------- |     |\/ 3 *3 /   -------------------- + ---------------------------                                             ___                            |
 325413     |                             48041841811*\/ 3                                      \/    28490909537802128272          94023741269056       |     |      \/    28490909537802128272          94023741269056                                     48041841811*\/ 3                             |
------- + I*|- ------------------------------------------------------------------------ - ---------------------------------------------------------------| + I*|--------------------------------------------------------------- + ------------------------------------------------------------------------|
4848292     |                      ____________________________________________________                                  6                               |     |                               6                                                      ____________________________________________________|
            |                     /                            _______________________                                                                   |     |                                                                                     /                            _______________________ |
            |                    /    217400660807751      3*\/ 226481291323535624673                                                                    |     |                                                                                    /    217400660807751      3*\/ 226481291323535624673  |
            |  47011870634528*3 /   -------------------- + ---------------------------                                                                   |     |                                                                  47011870634528*3 /   -------------------- + --------------------------- |
            \                 \/    28490909537802128272          94023741269056                                                                         /     \                                                                                 \/    28490909537802128272          94023741269056       /
3254134848292+i(−321740066080775128490909537802128272+32264812913235356246739402374126905636−4804184181134701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563)+i(4804184181134701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563+321740066080775128490909537802128272+32264812913235356246739402374126905636)\frac{325413}{4848292} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} - \frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}\right) + i \left(\frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6}\right) 
producto
/                                                                                          ____________________________________________________     /           ____________________________________________________                                                                           \\ /                                                                                          ____________________________________________________     /                                                                                        ____________________________________________________\\ /               ____________________________________________________                                                                           \
|                                                                                         /                            _______________________      |          /                            _______________________                                                                            || |                                                                                         /                            _______________________      |                                                                                       /                            _______________________ || |              /                            _______________________                                                                            |
|                                                                                        /    217400660807751      3*\/ 226481291323535624673       |  ___    /    217400660807751      3*\/ 226481291323535624673                                                                             || |                                                                                        /    217400660807751      3*\/ 226481291323535624673       |                                                                               ___    /    217400660807751      3*\/ 226481291323535624673  || |             /    217400660807751      3*\/ 226481291323535624673                                                                             |
|                                                                                     3 /   -------------------- + ---------------------------      |\/ 3 *3 /   -------------------- + ---------------------------                                             ___                            || |                                                                                     3 /   -------------------- + ---------------------------      |                                           ___                               \/ 3 *3 /   -------------------- + --------------------------- || |          3 /   -------------------- + ---------------------------                                                                            |
| 108471                                 48041841811                                  \/    28490909537802128272          94023741269056            |      \/    28490909537802128272          94023741269056                                     48041841811*\/ 3                             || | 108471                                 48041841811                                  \/    28490909537802128272          94023741269056            |                             48041841811*\/ 3                                      \/    28490909537802128272          94023741269056       || | 108471   \/    28490909537802128272          94023741269056                                        48041841811                               |
|------- - ------------------------------------------------------------------------ + --------------------------------------------------------- + I*|--------------------------------------------------------------- + ------------------------------------------------------------------------||*|------- - ------------------------------------------------------------------------ + --------------------------------------------------------- + I*|- ------------------------------------------------------------------------ - ---------------------------------------------------------------||*|------- - --------------------------------------------------------- + ------------------------------------------------------------------------|
|4848292                       ____________________________________________________                               6                                 |                               6                                                      ____________________________________________________|| |4848292                       ____________________________________________________                               6                                 |                      ____________________________________________________                                  6                               || |4848292                               3                                                   ____________________________________________________|
|                             /                            _______________________                                                                  |                                                                                     /                            _______________________ || |                             /                            _______________________                                                                  |                     /                            _______________________                                                                   || |                                                                                         /                            _______________________ |
|                            /    217400660807751      3*\/ 226481291323535624673                                                                   |                                                                                    /    217400660807751      3*\/ 226481291323535624673  || |                            /    217400660807751      3*\/ 226481291323535624673                                                                   |                    /    217400660807751      3*\/ 226481291323535624673                                                                    || |                                                                                        /    217400660807751      3*\/ 226481291323535624673  |
|          47011870634528*3 /   -------------------- + ---------------------------                                                                  |                                                                  47011870634528*3 /   -------------------- + --------------------------- || |          47011870634528*3 /   -------------------- + ---------------------------                                                                  |  47011870634528*3 /   -------------------- + ---------------------------                                                                   || |                                                                      23505935317264*3 /   -------------------- + --------------------------- |
\                         \/    28490909537802128272          94023741269056                                                                        \                                                                                 \/    28490909537802128272          94023741269056       // \                         \/    28490909537802128272          94023741269056                                                                        \                 \/    28490909537802128272          94023741269056                                                                         // \                                                                                     \/    28490909537802128272          94023741269056       /
(−480418418114701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563+21740066080775128490909537802128272+32264812913235356246739402374126905636+1084714848292+i(4804184181134701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563+321740066080775128490909537802128272+32264812913235356246739402374126905636))(−480418418114701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563+21740066080775128490909537802128272+32264812913235356246739402374126905636+1084714848292+i(−321740066080775128490909537802128272+32264812913235356246739402374126905636−4804184181134701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563))(−21740066080775128490909537802128272+32264812913235356246739402374126905633+1084714848292+480418418112350593531726421740066080775128490909537802128272+3226481291323535624673940237412690563)\left(- \frac{48041841811}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} + \frac{108471}{4848292} + i \left(\frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6}\right)\right) \left(- \frac{48041841811}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} + \frac{108471}{4848292} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} - \frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{3} + \frac{108471}{4848292} + \frac{48041841811}{23505935317264 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}\right) 
=
  1093  
--------
19393168
109319393168\frac{1093}{19393168} 
1093/19393168
Respuesta rápida [src] 
                                                                                               ____________________________________________________     /           ____________________________________________________                                                                           \
                                                                                              /                            _______________________      |          /                            _______________________                                                                            |
                                                                                             /    217400660807751      3*\/ 226481291323535624673       |  ___    /    217400660807751      3*\/ 226481291323535624673                                                                             |
                                                                                          3 /   -------------------- + ---------------------------      |\/ 3 *3 /   -------------------- + ---------------------------                                             ___                            |
      108471                                 48041841811                                  \/    28490909537802128272          94023741269056            |      \/    28490909537802128272          94023741269056                                     48041841811*\/ 3                             |
t1 = ------- - ------------------------------------------------------------------------ + --------------------------------------------------------- + I*|--------------------------------------------------------------- + ------------------------------------------------------------------------|
     4848292                       ____________________________________________________                               6                                 |                               6                                                      ____________________________________________________|
                                  /                            _______________________                                                                  |                                                                                     /                            _______________________ |
                                 /    217400660807751      3*\/ 226481291323535624673                                                                   |                                                                                    /    217400660807751      3*\/ 226481291323535624673  |
               47011870634528*3 /   -------------------- + ---------------------------                                                                  |                                                                  47011870634528*3 /   -------------------- + --------------------------- |
                              \/    28490909537802128272          94023741269056                                                                        \                                                                                 \/    28490909537802128272          94023741269056       /
t1=−480418418114701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563+21740066080775128490909537802128272+32264812913235356246739402374126905636+1084714848292+i(4804184181134701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563+321740066080775128490909537802128272+32264812913235356246739402374126905636)t_{1} = - \frac{48041841811}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} + \frac{108471}{4848292} + i \left(\frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6}\right) 
                                                                                               ____________________________________________________     /                                                                                        ____________________________________________________\
                                                                                              /                            _______________________      |                                                                                       /                            _______________________ |
                                                                                             /    217400660807751      3*\/ 226481291323535624673       |                                                                               ___    /    217400660807751      3*\/ 226481291323535624673  |
                                                                                          3 /   -------------------- + ---------------------------      |                                           ___                               \/ 3 *3 /   -------------------- + --------------------------- |
      108471                                 48041841811                                  \/    28490909537802128272          94023741269056            |                             48041841811*\/ 3                                      \/    28490909537802128272          94023741269056       |
t2 = ------- - ------------------------------------------------------------------------ + --------------------------------------------------------- + I*|- ------------------------------------------------------------------------ - ---------------------------------------------------------------|
     4848292                       ____________________________________________________                               6                                 |                      ____________________________________________________                                  6                               |
                                  /                            _______________________                                                                  |                     /                            _______________________                                                                   |
                                 /    217400660807751      3*\/ 226481291323535624673                                                                   |                    /    217400660807751      3*\/ 226481291323535624673                                                                    |
               47011870634528*3 /   -------------------- + ---------------------------                                                                  |  47011870634528*3 /   -------------------- + ---------------------------                                                                   |
                              \/    28490909537802128272          94023741269056                                                                        \                 \/    28490909537802128272          94023741269056                                                                         /
t2=−480418418114701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563+21740066080775128490909537802128272+32264812913235356246739402374126905636+1084714848292+i(−321740066080775128490909537802128272+32264812913235356246739402374126905636−4804184181134701187063452821740066080775128490909537802128272+3226481291323535624673940237412690563)t_{2} = - \frac{48041841811}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} + \frac{108471}{4848292} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} - \frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}\right) 
                    ____________________________________________________                                                                           
                   /                            _______________________                                                                            
                  /    217400660807751      3*\/ 226481291323535624673                                                                             
               3 /   -------------------- + ---------------------------                                                                            
      108471   \/    28490909537802128272          94023741269056                                        48041841811                               
t3 = ------- - --------------------------------------------------------- + ------------------------------------------------------------------------
     4848292                               3                                                   ____________________________________________________
                                                                                              /                            _______________________ 
                                                                                             /    217400660807751      3*\/ 226481291323535624673  
                                                                           23505935317264*3 /   -------------------- + --------------------------- 
                                                                                          \/    28490909537802128272          94023741269056
t3=−21740066080775128490909537802128272+32264812913235356246739402374126905633+1084714848292+480418418112350593531726421740066080775128490909537802128272+3226481291323535624673940237412690563t_{3} = - \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{3} + \frac{108471}{4848292} + \frac{48041841811}{23505935317264 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} 
t3 = -(217400660807751/28490909537802128272 + 3*sqrt(226481291323535624673)/94023741269056)^(1/3)/3 + 108471/4848292 + 48041841811/(23505935317264*(217400660807751/28490909537802128272 + 3*sqrt(226481291323535624673)/94023741269056)^(1/3))
Respuesta numérica [src] 
t1 = 0.0225113050563362 + 0.0452092341321696*i
t2 = 0.0220964907995664
t3 = 0.0225113050563362 - 0.0452092341321696*i
t3 = 0.0225113050563362 - 0.0452092341321696*i
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