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- La ecuación:
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Ecuación x^2+5x=36
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Ecuación 9-7(x+3)=5-6x
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Ecuación 4x-5=3+2(x+1)
-
Ecuación 6/(x-2)+5/x=3
- Expresar {x} en función de y en la ecuación:
- -14*x-12*y=-13
- -20*x+14*y=16
- -7*x+15*y=-11
- -14*x+5*y=3
-
Expresiones idénticas
- x^ tres +(ciento noventa y cinco , doscientos seis * diez mil ciento veinticinco /(dos * sesenta * trescientos treinta y siete , cinco ^ dos)- trescientos treinta y siete , cinco)*x^ dos -(ciento noventa y cinco , doscientos seis * sesenta y siete mil quinientos / ciento veinte)= cero
- x al cubo más (195,206 multiplicar por 10125 dividir por (2 multiplicar por 60 multiplicar por 337,5 al cuadrado ) menos 337,5) multiplicar por x al cuadrado menos (195,206 multiplicar por 67500 dividir por 120) es igual a 0
- x en el grado tres más (ciento noventa y cinco , doscientos seis multiplicar por diez mil ciento veinticinco dividir por (dos multiplicar por sesenta multiplicar por trescientos treinta y siete , cinco en el grado dos) menos trescientos treinta y siete , cinco) multiplicar por x en el grado dos menos (ciento noventa y cinco , doscientos seis multiplicar por sesenta y siete mil quinientos dividir por ciento veinte) es igual a cero
- x3+(195,206*10125/(2*60*337,52)-337,5)*x2-(195,206*67500/120)=0
- x3+195,206*10125/2*60*337,52-337,5*x2-195,206*67500/120=0
- x³+(195,206*10125/(2*60*337,5²)-337,5)*x²-(195,206*67500/120)=0
- x en el grado 3+(195,206*10125/(2*60*337,5 en el grado 2)-337,5)*x en el grado 2-(195,206*67500/120)=0
- x^3+(195,20610125/(260337,5^2)-337,5)x^2-(195,20667500/120)=0
- x3+(195,20610125/(260337,52)-337,5)x2-(195,20667500/120)=0
- x3+195,20610125/260337,52-337,5x2-195,20667500/120=0
- x^3+195,20610125/260337,5^2-337,5x^2-195,20667500/120=0
- x^3+(195,206*10125/(2*60*337,5^2)-337,5)*x^2-(195,206*67500/120)=O
- x^3+(195,206*10125 dividir por (2*60*337,5^2)-337,5)*x^2-(195,206*67500 dividir por 120)=0
-
Expresiones semejantes
- x^3+(195,206*10125/(2*60*337,5^2)-337,5)*x^2+(195,206*67500/120)=0
- x^3+(195,206*10125/(2*60*337,5^2)+337,5)*x^2-(195,206*67500/120)=0
- x^3-(195,206*10125/(2*60*337,5^2)-337,5)*x^2-(195,206*67500/120)=0
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
Ha introducido
[src]
//97603*10125\ \
||-----------| |
3 |\ 500 / 675| 2 1125*(-97603)
x + |------------- - ---|*x + ------------- = 0
| 2 2 | 2*500
\ 120*675/2 /
$$\left(x^{3} + x^{2} \left(- \frac{675}{2} + \frac{\frac{97603}{500} \cdot 10125}{120 \left(\frac{675}{2}\right)^{2}}\right)\right) + \frac{\left(-97603\right) 1125}{2 \cdot 500} = 0$$
Teorema de Cardano-Vieta
es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{227714897}{675000}$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = \frac{\left(-97603\right) 1125}{2 \cdot 500}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = \frac{227714897}{675000}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = \frac{\left(-97603\right) 1125}{2 \cdot 500}$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{227714897}{675000}$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = \frac{\left(-97603\right) 1125}{2 \cdot 500}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = \frac{227714897}{675000}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = \frac{\left(-97603\right) 1125}{2 \cdot 500}$$
Respuesta rápida
[src]
__________________________________________________________________ / __________________________________________________________________ \
/ _________________________________ | / _________________________________ |
/ 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 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} - \frac{51854074315720609}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} + \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}\right)$$
__________________________________________________________________ / __________________________________________________________________ \
/ _________________________________ | / _________________________________ |
/ 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 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} - \frac{51854074315720609}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + i \left(- \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2}\right)$$
__________________________________________________________________
/ _________________________________
227714897 / 12263835937251656146712273 \/ 5873695133855530253246383658095 51854074315720609
x3 = --------- + 3 / -------------------------- + ----------------------------------- + -------------------------------------------------------------------------------------
2025000 \/ 8303765625000000000 6075000000 __________________________________________________________________
/ _________________________________
/ 12263835937251656146712273 \/ 5873695133855530253246383658095
4100625000000*3 / -------------------------- + -----------------------------------
\/ 8303765625000000000 6075000000
$$x_{3} = \frac{51854074315720609}{4100625000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}$$
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]
suma
__________________________________________________________________ / __________________________________________________________________ \ __________________________________________________________________ / __________________________________________________________________ \
/ _________________________________ | / _________________________________ | / _________________________________ | / _________________________________ |
/ 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
$$\left(\frac{51854074315720609}{4100625000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} - \frac{51854074315720609}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} + \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} - \frac{51854074315720609}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + i \left(- \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2}\right)\right)\right)$$
=
/ __________________________________________________________________ \ / __________________________________________________________________ \
| / _________________________________ | | / _________________________________ |
| ___ / 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 /
$$\frac{227714897}{675000} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} + \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}\right) + i \left(- \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2}\right)$$
producto
/ __________________________________________________________________ / __________________________________________________________________ \\ / __________________________________________________________________ / __________________________________________________________________ \\ | / _________________________________ | / _________________________________ || | / _________________________________ | / _________________________________ || | / 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 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} - \frac{51854074315720609}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + i \left(- \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} - \frac{51854074315720609}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}{2} + \frac{51854074315720609 \sqrt{3}}{8201250000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}}\right)\right) \left(\frac{51854074315720609}{4100625000000 \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}} + \frac{227714897}{2025000} + \sqrt[3]{\frac{\sqrt{5873695133855530253246383658095}}{6075000000} + \frac{12263835937251656146712273}{8303765625000000000}}\right)$$
=
878427/8
$$\frac{878427}{8}$$
878427/8
Respuesta numérica
[src]
x1 = -0.479671415379271 + 18.0091571499161*i
x2 = 338.314745793721
x3 = -0.479671415379271 - 18.0091571499161*i
x3 = -0.479671415379271 - 18.0091571499161*i