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- La ecuación:
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Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
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Ecuación x^2+4=5x
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Ecuación x(x^2+2x+1)=6(x+1)
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Ecuación 4x+1=-3x+15
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -9*x+11*y=9
- -4*x-8*y=-20
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Expresiones idénticas
- (x^ cuatro - cuatro x+ uno)/(x-4)= cero
- (x en el grado 4 menos 4x más 1) dividir por (x menos 4) es igual a 0
- (x en el grado cuatro menos cuatro x más uno) dividir por (x menos 4) es igual a cero
- (x4-4x+1)/(x-4)=0
- x4-4x+1/x-4=0
- (x⁴-4x+1)/(x-4)=0
- x^4-4x+1/x-4=0
- (x^4-4x+1)/(x-4)=O
- (x^4-4x+1) dividir por (x-4)=0
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Expresiones semejantes
- (x^4-4x-1)/(x-4)=0
- (x^4+4x+1)/(x-4)=0
- (x^4-4x+1)/(x+4)=0
(x^4-4x+1)/(x-4)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
4 x - 4*x + 1 ------------ = 0 x - 4
$$\frac{\left(x^{4} - 4 x\right) + 1}{x - 4} = 0$$
Suma y producto de raíces
[src]
suma
_____________________________________________________________________________________________________ _____________________________________________________________________________________________________ ___________________________________________________________________________________________________ ___________________________________________________________________________________________________
/ ____________ / ____________ / ____________ / ____________
/ / ____ / / ____ / / ____ / / ____
/ / \/ 78 8 2 / / \/ 78 8 2 / / \/ 78 8 2 / / \/ 78 8 2
/ - 2*3 / 1 + ------ + ----------------------------------------------------- - ------------------- / - 2*3 / 1 + ------ + ----------------------------------------------------- - ------------------- I* / 2*3 / 1 + ------ + ----------------------------------------------------- + ------------------- I* / 2*3 / 1 + ------ + ----------------------------------------------------- + -------------------
___________________________________________ / \/ 9 ___________________________________________ ____________ ___________________________________________ / \/ 9 ___________________________________________ ____________ ___________________________________________ / \/ 9 ___________________________________________ ____________ ___________________________________________ / \/ 9 ___________________________________________ ____________
/ ____________ / / ____________ / ____ / ____________ / / ____________ / ____ / ____________ / / ____________ / ____ / ____________ / / ____________ / ____
/ / ____ / / / ____ / \/ 78 / / ____ / / / ____ / \/ 78 / / ____ / / / ____ / \/ 78 / / ____ / / / ____ / \/ 78
/ / \/ 78 2 / / / \/ 78 2 3*3 / 1 + ------ / / \/ 78 2 / / / \/ 78 2 3*3 / 1 + ------ / / \/ 78 2 / / / \/ 78 2 3*3 / 1 + ------ / / \/ 78 2 / / / \/ 78 2 3*3 / 1 + ------
/ 2*3 / 1 + ------ + ------------------- / / 2*3 / 1 + ------ + ------------------- \/ 9 / 2*3 / 1 + ------ + ------------------- / / 2*3 / 1 + ------ + ------------------- \/ 9 / 2*3 / 1 + ------ + ------------------- / / 2*3 / 1 + ------ + ------------------- \/ 9 / 2*3 / 1 + ------ + ------------------- / / 2*3 / 1 + ------ + ------------------- \/ 9
/ \/ 9 ____________ / / \/ 9 ____________ / \/ 9 ____________ / / \/ 9 ____________ / \/ 9 ____________ / / \/ 9 ____________ / \/ 9 ____________ / / \/ 9 ____________
/ / ____ / / / ____ / / ____ / / / ____ / / ____ / / / ____ / / ____ / / / ____
/ / \/ 78 / / / \/ 78 / / \/ 78 / / / \/ 78 / / \/ 78 / / / \/ 78 / / \/ 78 / / / \/ 78
/ 3*3 / 1 + ------ / / 3*3 / 1 + ------ / 3*3 / 1 + ------ / / 3*3 / 1 + ------ / 3*3 / 1 + ------ / / 3*3 / 1 + ------ / 3*3 / 1 + ------ / / 3*3 / 1 + ------
\/ \/ 9 \/ \/ \/ 9 \/ \/ 9 \/ \/ \/ 9 \/ \/ 9 \/ \/ \/ 9 \/ \/ 9 \/ \/ \/ 9
----------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- + - ----------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- + - ----------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------
2 2 2 2 2 2 2 2
$$\left(\left(\left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + \frac{8}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}}}{2} + \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}{2}\right) + \left(\frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + \frac{8}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}}}{2} + \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}{2}\right)\right) + \left(- \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}{2} - \frac{i \sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1} + \frac{8}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}}}{2}\right)\right) + \left(- \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}{2} + \frac{i \sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1} + \frac{8}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}}}{2}\right)$$
=
0
$$0$$
producto
/ _____________________________________________________________________________________________________\ / _____________________________________________________________________________________________________\ / ___________________________________________________________________________________________________\ / ___________________________________________________________________________________________________\ | / ____________ | | / ____________ | | / ____________ | | / ____________ | | / / ____ | | / / ____ | | / / ____ | | / / ____ | | / / \/ 78 8 2 | | / / \/ 78 8 2 | | / / \/ 78 8 2 | | / / \/ 78 8 2 | | / - 2*3 / 1 + ------ + ----------------------------------------------------- - ------------------- | | / - 2*3 / 1 + ------ + ----------------------------------------------------- - ------------------- | | I* / 2*3 / 1 + ------ + ----------------------------------------------------- + ------------------- | | I* / 2*3 / 1 + ------ + ----------------------------------------------------- + ------------------- | | ___________________________________________ / \/ 9 ___________________________________________ ____________ | | ___________________________________________ / \/ 9 ___________________________________________ ____________ | | ___________________________________________ / \/ 9 ___________________________________________ ____________ | | ___________________________________________ / \/ 9 ___________________________________________ ____________ | | / ____________ / / ____________ / ____ | | / ____________ / / ____________ / ____ | | / ____________ / / ____________ / ____ | | / ____________ / / ____________ / ____ | | / / ____ / / / ____ / \/ 78 | | / / ____ / / / ____ / \/ 78 | | / / ____ / / / ____ / \/ 78 | | / / ____ / / / ____ / \/ 78 | | / / \/ 78 2 / / / \/ 78 2 3*3 / 1 + ------ | | / / \/ 78 2 / / / \/ 78 2 3*3 / 1 + ------ | | / / \/ 78 2 / / / \/ 78 2 3*3 / 1 + ------ | | / / \/ 78 2 / / / \/ 78 2 3*3 / 1 + ------ | | / 2*3 / 1 + ------ + ------------------- / / 2*3 / 1 + ------ + ------------------- \/ 9 | | / 2*3 / 1 + ------ + ------------------- / / 2*3 / 1 + ------ + ------------------- \/ 9 | | / 2*3 / 1 + ------ + ------------------- / / 2*3 / 1 + ------ + ------------------- \/ 9 | | / 2*3 / 1 + ------ + ------------------- / / 2*3 / 1 + ------ + ------------------- \/ 9 | | / \/ 9 ____________ / / \/ 9 ____________ | | / \/ 9 ____________ / / \/ 9 ____________ | | / \/ 9 ____________ / / \/ 9 ____________ | | / \/ 9 ____________ / / \/ 9 ____________ | | / / ____ / / / ____ | | / / ____ / / / ____ | | / / ____ / / / ____ | | / / ____ / / / ____ | | / / \/ 78 / / / \/ 78 | | / / \/ 78 / / / \/ 78 | | / / \/ 78 / / / \/ 78 | | / / \/ 78 / / / \/ 78 | | / 3*3 / 1 + ------ / / 3*3 / 1 + ------ | | / 3*3 / 1 + ------ / / 3*3 / 1 + ------ | | / 3*3 / 1 + ------ / / 3*3 / 1 + ------ | | / 3*3 / 1 + ------ / / 3*3 / 1 + ------ | |\/ \/ 9 \/ \/ \/ 9 | |\/ \/ 9 \/ \/ \/ 9 | | \/ \/ 9 \/ \/ \/ 9 | | \/ \/ 9 \/ \/ \/ 9 | |----------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------|*|----------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------|*|- ----------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------|*|- ----------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------| \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 /
$$\left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + \frac{8}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}}}{2} + \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}{2}\right) \left(\frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + \frac{8}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}}}{2} + \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}{2}\right) \left(- \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}{2} - \frac{i \sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1} + \frac{8}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}}}{2}\right) \left(- \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}{2} + \frac{i \sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1} + \frac{8}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}}}{2}\right)$$
=
1
$$1$$
1
Respuesta rápida
[src]
_____________________________________________________________________________________________________
/ ____________
/ / ____
/ / \/ 78 8 2
/ - 2*3 / 1 + ------ + ----------------------------------------------------- - -------------------
___________________________________________ / \/ 9 ___________________________________________ ____________
/ ____________ / / ____________ / ____
/ / ____ / / / ____ / \/ 78
/ / \/ 78 2 / / / \/ 78 2 3*3 / 1 + ------
/ 2*3 / 1 + ------ + ------------------- / / 2*3 / 1 + ------ + ------------------- \/ 9
/ \/ 9 ____________ / / \/ 9 ____________
/ / ____ / / / ____
/ / \/ 78 / / / \/ 78
/ 3*3 / 1 + ------ / / 3*3 / 1 + ------
\/ \/ 9 \/ \/ \/ 9
x1 = ----------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------
2 2
$$x_{1} = - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + \frac{8}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}}}{2} + \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}{2}$$
_____________________________________________________________________________________________________
/ ____________
/ / ____
/ / \/ 78 8 2
/ - 2*3 / 1 + ------ + ----------------------------------------------------- - -------------------
___________________________________________ / \/ 9 ___________________________________________ ____________
/ ____________ / / ____________ / ____
/ / ____ / / / ____ / \/ 78
/ / \/ 78 2 / / / \/ 78 2 3*3 / 1 + ------
/ 2*3 / 1 + ------ + ------------------- / / 2*3 / 1 + ------ + ------------------- \/ 9
/ \/ 9 ____________ / / \/ 9 ____________
/ / ____ / / / ____
/ / \/ 78 / / / \/ 78
/ 3*3 / 1 + ------ / / 3*3 / 1 + ------
\/ \/ 9 \/ \/ \/ 9
x2 = ----------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------
2 2
$$x_{2} = \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1} - \frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + \frac{8}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}}}{2} + \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}{2}$$
___________________________________________________________________________________________________
/ ____________
/ / ____
/ / \/ 78 8 2
I* / 2*3 / 1 + ------ + ----------------------------------------------------- + -------------------
___________________________________________ / \/ 9 ___________________________________________ ____________
/ ____________ / / ____________ / ____
/ / ____ / / / ____ / \/ 78
/ / \/ 78 2 / / / \/ 78 2 3*3 / 1 + ------
/ 2*3 / 1 + ------ + ------------------- / / 2*3 / 1 + ------ + ------------------- \/ 9
/ \/ 9 ____________ / / \/ 9 ____________
/ / ____ / / / ____
/ / \/ 78 / / / \/ 78
/ 3*3 / 1 + ------ / / 3*3 / 1 + ------
\/ \/ 9 \/ \/ \/ 9
x3 = - ----------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------
2 2
$$x_{3} = - \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}{2} - \frac{i \sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1} + \frac{8}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}}}{2}$$
___________________________________________________________________________________________________
/ ____________
/ / ____
/ / \/ 78 8 2
I* / 2*3 / 1 + ------ + ----------------------------------------------------- + -------------------
___________________________________________ / \/ 9 ___________________________________________ ____________
/ ____________ / / ____________ / ____
/ / ____ / / / ____ / \/ 78
/ / \/ 78 2 / / / \/ 78 2 3*3 / 1 + ------
/ 2*3 / 1 + ------ + ------------------- / / 2*3 / 1 + ------ + ------------------- \/ 9
/ \/ 9 ____________ / / \/ 9 ____________
/ / ____ / / / ____
/ / \/ 78 / / / \/ 78
/ 3*3 / 1 + ------ / / 3*3 / 1 + ------
\/ \/ 9 \/ \/ \/ 9
x4 = - ----------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------
2 2
$$x_{4} = - \frac{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}{2} + \frac{i \sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1} + \frac{8}{\sqrt{\frac{2}{3 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}} + 2 \sqrt[3]{\frac{\sqrt{78}}{9} + 1}}}}}{2}$$
x4 = -sqrt(2/(3*(sqrt(78)/9 + 1)^(1/3)) + 2*(sqrt(78)/9 + 1)^(1/3))/2 + i*sqrt(2/(3*(sqrt(78)/9 + 1)^(1/3)) + 2*(sqrt(78)/9 + 1)^(1/3) + 8/sqrt(2/(3*(sqrt(78)/9 + 1)^(1/3)) + 2*(sqrt(78)/9 + 1)^(1/3)))/2
Respuesta numérica
[src]
x1 = -0.872175357025343 - 1.38103159782422*i
x2 = -0.872175357025343 + 1.38103159782422*i
x3 = 0.250992157490491
x4 = 1.49335855656019
x4 = 1.49335855656019