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- La ecuación:
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Ecuación x=-x
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Ecuación 3x+5=x
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Ecuación x^2-5x+6=0
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Ecuación x^2+2*x+1=0
- Expresar {x} en función de y en la ecuación:
- 9*x+7*y=4
- 2*x+5*y=1
- -1*x+11*y=16
- -3*x-9*y=16
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Expresiones idénticas
- (quince mil trescientos setenta y seis . cero *t- trescientos ochenta y ocho . cero)*(- setenta . cero *t+(- sesenta y dos . cero *t+ uno . cero)^ dos + ocho . cero)+(diecinueve mil seiscientos . cero *t- cuatrocientos cuatro . cero)*(- sesenta y dos . cero *t+(- setenta . cero *t+ uno . cero)^ dos + doce . cero)= cero
- (15376.0 multiplicar por t menos 388.0) multiplicar por ( menos 70.0 multiplicar por t más ( menos 62.0 multiplicar por t más 1.0) al cuadrado más 8.0) más (19600.0 multiplicar por t menos 404.0) multiplicar por ( menos 62.0 multiplicar por t más ( menos 70.0 multiplicar por t más 1.0) al cuadrado más 12.0) es igual a 0
- (quince mil trescientos setenta y seis . cero multiplicar por t menos trescientos ochenta y ocho . cero) multiplicar por ( menos setenta . cero multiplicar por t más ( menos sesenta y dos . cero multiplicar por t más uno . cero) en el grado dos más ocho . cero) más (diecinueve mil seiscientos . cero multiplicar por t menos cuatrocientos cuatro . cero) multiplicar por ( menos sesenta y dos . cero multiplicar por t más ( menos setenta . cero multiplicar por t más uno . cero) en el grado dos más doce . cero) es igual a cero
- (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
- 15376.0*t-388.0*-70.0*t+-62.0*t+1.02+8.0+19600.0*t-404.0*-62.0*t+-70.0*t+1.02+12.0=0
- (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
- (15376.0*t-388.0)*(-70.0*t+(-62.0*t+1.0) en el grado 2+8.0)+(19600.0*t-404.0)*(-62.0*t+(-70.0*t+1.0) en el grado 2+12.0)=0
- (15376.0t-388.0)(-70.0t+(-62.0t+1.0)^2+8.0)+(19600.0t-404.0)(-62.0t+(-70.0t+1.0)^2+12.0)=0
- (15376.0t-388.0)(-70.0t+(-62.0t+1.0)2+8.0)+(19600.0t-404.0)(-62.0t+(-70.0t+1.0)2+12.0)=0
- 15376.0t-388.0-70.0t+-62.0t+1.02+8.0+19600.0t-404.0-62.0t+-70.0t+1.02+12.0=0
- 15376.0t-388.0-70.0t+-62.0t+1.0^2+8.0+19600.0t-404.0-62.0t+-70.0t+1.0^2+12.0=0
- (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)=O
-
Expresiones semejantes
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
(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
El profesor se sorprenderá mucho al ver tu solución correcta😉
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
$$\left(15376 t - 388\right) \left(\left(- 70 t + \left(1 - 62 t\right)^{2}\right) + 8\right) + \left(19600 t - 404\right) \left(\left(- 62 t + \left(1 - 70 t\right)^{2}\right) + 12\right) = 0$$
Suma y producto de raíces
[src]
suma
____________________________________________________ / ____________________________________________________ \ ____________________________________________________ / ____________________________________________________\ ____________________________________________________
/ _______________________ | / _______________________ | / _______________________ | / _______________________ | / _______________________
/ 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
$$\left(- \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{3} + \frac{108471}{4848292} + \frac{48041841811}{23505935317264 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}\right) + \left(\left(- \frac{48041841811}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} + \frac{108471}{4848292} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} - \frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}\right)\right) + \left(- \frac{48041841811}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} + \frac{108471}{4848292} + i \left(\frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6}\right)\right)\right)$$
=
/ ____________________________________________________\ / ____________________________________________________ \
| / _______________________ | | / _______________________ |
| ___ / 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 /
$$\frac{325413}{4848292} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} - \frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}\right) + i \left(\frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6}\right)$$
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 /
$$\left(- \frac{48041841811}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} + \frac{108471}{4848292} + i \left(\frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6}\right)\right) \left(- \frac{48041841811}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} + \frac{108471}{4848292} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} - \frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{3} + \frac{108471}{4848292} + \frac{48041841811}{23505935317264 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}\right)$$
=
1093 -------- 19393168
$$\frac{1093}{19393168}$$
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 /
$$t_{1} = - \frac{48041841811}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} + \frac{108471}{4848292} + i \left(\frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6}\right)$$
____________________________________________________ / ____________________________________________________\
/ _______________________ | / _______________________ |
/ 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 /
$$t_{2} = - \frac{48041841811}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}} + \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} + \frac{108471}{4848292} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{6} - \frac{48041841811 \sqrt{3}}{47011870634528 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}\right)$$
____________________________________________________
/ _______________________
/ 217400660807751 3*\/ 226481291323535624673
3 / -------------------- + ---------------------------
108471 \/ 28490909537802128272 94023741269056 48041841811
t3 = ------- - --------------------------------------------------------- + ------------------------------------------------------------------------
4848292 3 ____________________________________________________
/ _______________________
/ 217400660807751 3*\/ 226481291323535624673
23505935317264*3 / -------------------- + ---------------------------
\/ 28490909537802128272 94023741269056
$$t_{3} = - \frac{\sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}{3} + \frac{108471}{4848292} + \frac{48041841811}{23505935317264 \sqrt[3]{\frac{217400660807751}{28490909537802128272} + \frac{3 \sqrt{226481291323535624673}}{94023741269056}}}$$
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