Sr Examen
x*(92-475+x)*(117-458+x)*(103-475+x)-(458-x)*(475-x)*(754-x)*(26+465-x)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
x*(-383 + x)*(-341 + x)*(-372 + x) - (458 - x)*(475 - x)*(754 - x)*(491 - x) = 0
$$x \left(x - 383\right) \left(x - 341\right) \left(x - 372\right) - \left(458 - x\right) \left(475 - x\right) \left(754 - x\right) \left(491 - x\right) = 0$$
Respuesta rápida
[src]
____________________________________________ / ____________________________________________\
/ ______________________ | / ______________________ |
/ 1420192098450 3*\/ 84422086514061747087 | ___ / 1420192098450 3*\/ 84422086514061747087 |
3 / ------------- + -------------------------- | ___ \/ 3 *3 / ------------- + -------------------------- |
224903 \/ 158340421 292681 604011747 | 604011747*\/ 3 \/ 158340421 292681 |
x1 = ------ - ------------------------------------------------- + -------------------------------------------------------- + I*|- -------------------------------------------------------- - -------------------------------------------------------|
541 2 ____________________________________________ | ____________________________________________ 2 |
/ ______________________ | / ______________________ |
/ 1420192098450 3*\/ 84422086514061747087 | / 1420192098450 3*\/ 84422086514061747087 |
585362*3 / ------------- + -------------------------- | 585362*3 / ------------- + -------------------------- |
\/ 158340421 292681 \ \/ 158340421 292681 /
$$x_{1} = - \frac{\sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2} + \frac{604011747}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}} + \frac{224903}{541} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2} - \frac{604011747 \sqrt{3}}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}\right)$$
____________________________________________ / ____________________________________________ \
/ ______________________ | / ______________________ |
/ 1420192098450 3*\/ 84422086514061747087 | ___ / 1420192098450 3*\/ 84422086514061747087 |
3 / ------------- + -------------------------- |\/ 3 *3 / ------------- + -------------------------- ___ |
224903 \/ 158340421 292681 604011747 | \/ 158340421 292681 604011747*\/ 3 |
x2 = ------ - ------------------------------------------------- + -------------------------------------------------------- + I*|------------------------------------------------------- + --------------------------------------------------------|
541 2 ____________________________________________ | 2 ____________________________________________|
/ ______________________ | / ______________________ |
/ 1420192098450 3*\/ 84422086514061747087 | / 1420192098450 3*\/ 84422086514061747087 |
585362*3 / ------------- + -------------------------- | 585362*3 / ------------- + -------------------------- |
\/ 158340421 292681 \ \/ 158340421 292681 /
$$x_{2} = - \frac{\sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2} + \frac{604011747}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}} + \frac{224903}{541} + i \left(\frac{604011747 \sqrt{3}}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}} + \frac{\sqrt{3} \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2}\right)$$
____________________________________________
/ ______________________
224903 / 1420192098450 3*\/ 84422086514061747087 604011747
x3 = ------ + 3 / ------------- + -------------------------- - --------------------------------------------------------
541 \/ 158340421 292681 ____________________________________________
/ ______________________
/ 1420192098450 3*\/ 84422086514061747087
292681*3 / ------------- + --------------------------
\/ 158340421 292681
$$x_{3} = - \frac{604011747}{292681 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}} + \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}} + \frac{224903}{541}$$
x3 = -604011747/(292681*(1420192098450/158340421 + 3*sqrt(84422086514061747087)/292681)^(1/3)) + (1420192098450/158340421 + 3*sqrt(84422086514061747087)/292681)^(1/3) + 224903/541
Suma y producto de raíces
[src]
suma
____________________________________________ / ____________________________________________\ ____________________________________________ / ____________________________________________ \
/ ______________________ | / ______________________ | / ______________________ | / ______________________ |
/ 1420192098450 3*\/ 84422086514061747087 | ___ / 1420192098450 3*\/ 84422086514061747087 | / 1420192098450 3*\/ 84422086514061747087 | ___ / 1420192098450 3*\/ 84422086514061747087 | ____________________________________________
3 / ------------- + -------------------------- | ___ \/ 3 *3 / ------------- + -------------------------- | 3 / ------------- + -------------------------- |\/ 3 *3 / ------------- + -------------------------- ___ | / ______________________
224903 \/ 158340421 292681 604011747 | 604011747*\/ 3 \/ 158340421 292681 | 224903 \/ 158340421 292681 604011747 | \/ 158340421 292681 604011747*\/ 3 | 224903 / 1420192098450 3*\/ 84422086514061747087 604011747
------ - ------------------------------------------------- + -------------------------------------------------------- + I*|- -------------------------------------------------------- - -------------------------------------------------------| + ------ - ------------------------------------------------- + -------------------------------------------------------- + I*|------------------------------------------------------- + --------------------------------------------------------| + ------ + 3 / ------------- + -------------------------- - --------------------------------------------------------
541 2 ____________________________________________ | ____________________________________________ 2 | 541 2 ____________________________________________ | 2 ____________________________________________| 541 \/ 158340421 292681 ____________________________________________
/ ______________________ | / ______________________ | / ______________________ | / ______________________ | / ______________________
/ 1420192098450 3*\/ 84422086514061747087 | / 1420192098450 3*\/ 84422086514061747087 | / 1420192098450 3*\/ 84422086514061747087 | / 1420192098450 3*\/ 84422086514061747087 | / 1420192098450 3*\/ 84422086514061747087
585362*3 / ------------- + -------------------------- | 585362*3 / ------------- + -------------------------- | 585362*3 / ------------- + -------------------------- | 585362*3 / ------------- + -------------------------- | 292681*3 / ------------- + --------------------------
\/ 158340421 292681 \ \/ 158340421 292681 / \/ 158340421 292681 \ \/ 158340421 292681 / \/ 158340421 292681
$$\left(- \frac{604011747}{292681 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}} + \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}} + \frac{224903}{541}\right) + \left(\left(- \frac{\sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2} + \frac{604011747}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}} + \frac{224903}{541} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2} - \frac{604011747 \sqrt{3}}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2} + \frac{604011747}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}} + \frac{224903}{541} + i \left(\frac{604011747 \sqrt{3}}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}} + \frac{\sqrt{3} \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2}\right)\right)\right)$$
=
/ ____________________________________________ \ / ____________________________________________\
| / ______________________ | | / ______________________ |
| ___ / 1420192098450 3*\/ 84422086514061747087 | | ___ / 1420192098450 3*\/ 84422086514061747087 |
|\/ 3 *3 / ------------- + -------------------------- ___ | | ___ \/ 3 *3 / ------------- + -------------------------- |
674709 | \/ 158340421 292681 604011747*\/ 3 | | 604011747*\/ 3 \/ 158340421 292681 |
------ + I*|------------------------------------------------------- + --------------------------------------------------------| + I*|- -------------------------------------------------------- - -------------------------------------------------------|
541 | 2 ____________________________________________| | ____________________________________________ 2 |
| / ______________________ | | / ______________________ |
| / 1420192098450 3*\/ 84422086514061747087 | | / 1420192098450 3*\/ 84422086514061747087 |
| 585362*3 / ------------- + -------------------------- | | 585362*3 / ------------- + -------------------------- |
\ \/ 158340421 292681 / \ \/ 158340421 292681 /
$$\frac{674709}{541} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2} - \frac{604011747 \sqrt{3}}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}\right) + i \left(\frac{604011747 \sqrt{3}}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}} + \frac{\sqrt{3} \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2}\right)$$
producto
/ ____________________________________________ / ____________________________________________\\ / ____________________________________________ / ____________________________________________ \\ | / ______________________ | / ______________________ || | / ______________________ | / ______________________ || | / 1420192098450 3*\/ 84422086514061747087 | ___ / 1420192098450 3*\/ 84422086514061747087 || | / 1420192098450 3*\/ 84422086514061747087 | ___ / 1420192098450 3*\/ 84422086514061747087 || / ____________________________________________ \ | 3 / ------------- + -------------------------- | ___ \/ 3 *3 / ------------- + -------------------------- || | 3 / ------------- + -------------------------- |\/ 3 *3 / ------------- + -------------------------- ___ || | / ______________________ | |224903 \/ 158340421 292681 604011747 | 604011747*\/ 3 \/ 158340421 292681 || |224903 \/ 158340421 292681 604011747 | \/ 158340421 292681 604011747*\/ 3 || |224903 / 1420192098450 3*\/ 84422086514061747087 604011747 | |------ - ------------------------------------------------- + -------------------------------------------------------- + I*|- -------------------------------------------------------- - -------------------------------------------------------||*|------ - ------------------------------------------------- + -------------------------------------------------------- + I*|------------------------------------------------------- + --------------------------------------------------------||*|------ + 3 / ------------- + -------------------------- - --------------------------------------------------------| | 541 2 ____________________________________________ | ____________________________________________ 2 || | 541 2 ____________________________________________ | 2 ____________________________________________|| | 541 \/ 158340421 292681 ____________________________________________| | / ______________________ | / ______________________ || | / ______________________ | / ______________________ || | / ______________________ | | / 1420192098450 3*\/ 84422086514061747087 | / 1420192098450 3*\/ 84422086514061747087 || | / 1420192098450 3*\/ 84422086514061747087 | / 1420192098450 3*\/ 84422086514061747087 || | / 1420192098450 3*\/ 84422086514061747087 | | 585362*3 / ------------- + -------------------------- | 585362*3 / ------------- + -------------------------- || | 585362*3 / ------------- + -------------------------- | 585362*3 / ------------- + -------------------------- || | 292681*3 / ------------- + -------------------------- | \ \/ 158340421 292681 \ \/ 158340421 292681 // \ \/ 158340421 292681 \ \/ 158340421 292681 // \ \/ 158340421 292681 /
$$\left(- \frac{\sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2} + \frac{604011747}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}} + \frac{224903}{541} + i \left(\frac{604011747 \sqrt{3}}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}} + \frac{\sqrt{3} \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2} + \frac{604011747}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}} + \frac{224903}{541} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}{2} - \frac{604011747 \sqrt{3}}{585362 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}}\right)\right) \left(- \frac{604011747}{292681 \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}}} + \sqrt[3]{\frac{1420192098450}{158340421} + \frac{3 \sqrt{84422086514061747087}}{292681}} + \frac{224903}{541}\right)$$
=
40270027850
-----------
541
$$\frac{40270027850}{541}$$
40270027850/541
Respuesta numérica
[src]
x1 = 414.270431105537 - 78.7238242369699*i
x2 = 418.610708953436
x3 = 414.270431105537 + 78.7238242369699*i
x3 = 414.270431105537 + 78.7238242369699*i