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Ecuación x^4=(x-20)^2
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Ecuación 5-2*(x-1)=4-x
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Ecuación (x+6)^3=25*(x+6)
- Ecuación x+y+2=0
- Expresar {x} en función de y en la ecuación:
- 10*x-18*y=3
- 16*x+7*y=8
- -19*x+1*y=0
- -11*x-15*y=14
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Expresiones idénticas
- uno *((x- dos)*(x- tres)*(x- cuatro)*(x- cinco))/ veinticuatro + trece *((x- uno)*(x- tres)*(x- cuatro)*(x- cinco))/(- seis)+ veintinueve *((x- uno)*(x- dos)*(x- cuatro)*(x- cinco))/ cuatro + cuarenta y nueve *((x- uno)*(x- dos)*(x- tres)*(x- cinco))/(- seis)+ setenta y tres *((x- uno)*(x- dos)*(x- tres)*(x- cuatro))/ veinticuatro = cero
- 1 multiplicar por ((x menos 2) multiplicar por (x menos 3) multiplicar por (x menos 4) multiplicar por (x menos 5)) dividir por 24 más 13 multiplicar por ((x menos 1) multiplicar por (x menos 3) multiplicar por (x menos 4) multiplicar por (x menos 5)) dividir por ( menos 6) más 29 multiplicar por ((x menos 1) multiplicar por (x menos 2) multiplicar por (x menos 4) multiplicar por (x menos 5)) dividir por 4 más 49 multiplicar por ((x menos 1) multiplicar por (x menos 2) multiplicar por (x menos 3) multiplicar por (x menos 5)) dividir por ( menos 6) más 73 multiplicar por ((x menos 1) multiplicar por (x menos 2) multiplicar por (x menos 3) multiplicar por (x menos 4)) dividir por 24 es igual a 0
- uno multiplicar por ((x menos dos) multiplicar por (x menos tres) multiplicar por (x menos cuatro) multiplicar por (x menos cinco)) dividir por veinticuatro más trece multiplicar por ((x menos uno) multiplicar por (x menos tres) multiplicar por (x menos cuatro) multiplicar por (x menos cinco)) dividir por ( menos seis) más veintinueve multiplicar por ((x menos uno) multiplicar por (x menos dos) multiplicar por (x menos cuatro) multiplicar por (x menos cinco)) dividir por cuatro más cuarenta y nueve multiplicar por ((x menos uno) multiplicar por (x menos dos) multiplicar por (x menos tres) multiplicar por (x menos cinco)) dividir por ( menos seis) más setenta y tres multiplicar por ((x menos uno) multiplicar por (x menos dos) multiplicar por (x menos tres) multiplicar por (x menos cuatro)) dividir por veinticuatro es igual a cero
- 1((x-2)(x-3)(x-4)(x-5))/24+13((x-1)(x-3)(x-4)(x-5))/(-6)+29((x-1)(x-2)(x-4)(x-5))/4+49((x-1)(x-2)(x-3)(x-5))/(-6)+73((x-1)(x-2)(x-3)(x-4))/24=0
- 1x-2x-3x-4x-5/24+13x-1x-3x-4x-5/-6+29x-1x-2x-4x-5/4+49x-1x-2x-3x-5/-6+73x-1x-2x-3x-4/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=O
- 1*((x-2)*(x-3)*(x-4)*(x-5)) dividir por 24+13*((x-1)*(x-3)*(x-4)*(x-5)) dividir por (-6)+29*((x-1)*(x-2)*(x-4)*(x-5)) dividir por 4+49*((x-1)*(x-2)*(x-3)*(x-5)) dividir por (-6)+73*((x-1)*(x-2)*(x-3)*(x-4)) dividir por 24=0
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Expresiones semejantes
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x+4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x+2)*(x-3)*(x-4))/24=0
- 1*((x+2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x+5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x+2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4-49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x+1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)-29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x+4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x+5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x+5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x+1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x+3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x+1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x+2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x+3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x+5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24-13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)-73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x+3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x+3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x+4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x+1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x+4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
(x - 2)*(x - 3)*(x - 4)*(x - 5) 13*(x - 1)*(x - 3)*(x - 4)*(x - 5) 29*(x - 1)*(x - 2)*(x - 4)*(x - 5) 49*(x - 1)*(x - 2)*(x - 3)*(x - 5) 73*(x - 1)*(x - 2)*(x - 3)*(x - 4)
------------------------------- + ---------------------------------- + ---------------------------------- + ---------------------------------- + ---------------------------------- = 0
24 -6 4 -6 24
$$\frac{73 \left(x - 2\right) \left(x - 1\right) \left(x - 3\right) \left(x - 4\right)}{24} + \left(\frac{49 \left(x - 2\right) \left(x - 1\right) \left(x - 3\right) \left(x - 5\right)}{-6} + \left(\frac{29 \left(x - 2\right) \left(x - 1\right) \left(x - 4\right) \left(x - 5\right)}{4} + \left(\frac{\left(x - 3\right) \left(x - 2\right) \left(x - 4\right) \left(x - 5\right)}{24} + \frac{13 \left(x - 3\right) \left(x - 1\right) \left(x - 4\right) \left(x - 5\right)}{-6}\right)\right)\right) = 0$$
Solución detallada
Abramos la expresión en la ecuación
$$\frac{73 \left(x - 2\right) \left(x - 1\right) \left(x - 3\right) \left(x - 4\right)}{24} + \left(\frac{49 \left(x - 2\right) \left(x - 1\right) \left(x - 3\right) \left(x - 5\right)}{-6} + \left(\frac{29 \left(x - 2\right) \left(x - 1\right) \left(x - 4\right) \left(x - 5\right)}{4} + \left(\frac{\left(x - 3\right) \left(x - 2\right) \left(x - 4\right) \left(x - 5\right)}{24} + \frac{13 \left(x - 3\right) \left(x - 1\right) \left(x - 4\right) \left(x - 5\right)}{-6}\right)\right)\right) = 0$$
Obtenemos la ecuación cuadrática
$$2 x^{2} + 6 x - 7 = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 2$$
$$b = 6$$
$$c = -7$$
, entonces
Como D > 0 la ecuación tiene dos raíces.
o
$$x_{1} = - \frac{3}{2} + \frac{\sqrt{23}}{2}$$
$$x_{2} = - \frac{\sqrt{23}}{2} - \frac{3}{2}$$
$$\frac{73 \left(x - 2\right) \left(x - 1\right) \left(x - 3\right) \left(x - 4\right)}{24} + \left(\frac{49 \left(x - 2\right) \left(x - 1\right) \left(x - 3\right) \left(x - 5\right)}{-6} + \left(\frac{29 \left(x - 2\right) \left(x - 1\right) \left(x - 4\right) \left(x - 5\right)}{4} + \left(\frac{\left(x - 3\right) \left(x - 2\right) \left(x - 4\right) \left(x - 5\right)}{24} + \frac{13 \left(x - 3\right) \left(x - 1\right) \left(x - 4\right) \left(x - 5\right)}{-6}\right)\right)\right) = 0$$
Obtenemos la ecuación cuadrática
$$2 x^{2} + 6 x - 7 = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 2$$
$$b = 6$$
$$c = -7$$
, entonces
D = b^2 - 4 * a * c =
(6)^2 - 4 * (2) * (-7) = 92
Como D > 0 la ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = - \frac{3}{2} + \frac{\sqrt{23}}{2}$$
$$x_{2} = - \frac{\sqrt{23}}{2} - \frac{3}{2}$$
Suma y producto de raíces
[src]
suma
____ ____ 3 \/ 23 3 \/ 23 - - + ------ + - - - ------ 2 2 2 2
$$\left(- \frac{\sqrt{23}}{2} - \frac{3}{2}\right) + \left(- \frac{3}{2} + \frac{\sqrt{23}}{2}\right)$$
=
-3
$$-3$$
producto
/ ____\ / ____\ | 3 \/ 23 | | 3 \/ 23 | |- - + ------|*|- - - ------| \ 2 2 / \ 2 2 /
$$\left(- \frac{3}{2} + \frac{\sqrt{23}}{2}\right) \left(- \frac{\sqrt{23}}{2} - \frac{3}{2}\right)$$
=
-7/2
$$- \frac{7}{2}$$
-7/2
Respuesta rápida
[src]
____
3 \/ 23
x1 = - - + ------
2 2
$$x_{1} = - \frac{3}{2} + \frac{\sqrt{23}}{2}$$
____
3 \/ 23
x2 = - - - ------
2 2
$$x_{2} = - \frac{\sqrt{23}}{2} - \frac{3}{2}$$
x2 = -sqrt(23)/2 - 3/2