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- La ecuación:
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Ecuación x^3-x^2-x-1=0
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Ecuación 3x-2(3x+4)=10
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Ecuación 12-4(x-3)=39-9x
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Ecuación 0,2x+2,7=1,4-1,1x
- Expresar {x} en función de y en la ecuación:
- -11*x-3*y=14
- 2*x-15*y=-1
- -18*x-6*y=-1
- 6*x+9*y=-9
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Expresiones idénticas
- (nueve / diez)*x-((siete / diez)*x+(tres / cinco)*y)* tres *y-x= nueve
- (9 dividir por 10) multiplicar por x menos ((7 dividir por 10) multiplicar por x más (3 dividir por 5) multiplicar por y) multiplicar por 3 multiplicar por y menos x es igual a 9
- (nueve dividir por diez) multiplicar por x menos ((siete dividir por diez) multiplicar por x más (tres dividir por cinco) multiplicar por y) multiplicar por tres multiplicar por y menos x es igual a nueve
- (9/10)x-((7/10)x+(3/5)y)3y-x=9
- 9/10x-7/10x+3/5y3y-x=9
- (9 dividir por 10)*x-((7 dividir por 10)*x+(3 dividir por 5)*y)*3*y-x=9
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Expresiones semejantes
- (9/10)*x-((7/10)*x-(3/5)*y)*3*y-x=9
- (9/10)*x-((7/10)*x+(3/5)*y)*3*y+x=9
- (9/10)*x+((7/10)*x+(3/5)*y)*3*y-x=9
(9/10)*x-((7/10)*x+(3/5)*y)*3*y-x=9 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
9*x /7*x 3*y\ --- - |--- + ---|*3*y - x = 9 10 \ 10 5 /
$$- x + \left(\frac{9 x}{10} - y 3 \left(\frac{7 x}{10} + \frac{3 y}{5}\right)\right) = 9$$
Solución detallada
Tenemos la ecuación:
Abrimos la expresión:
Reducimos, obtenemos:
Transportamos los términos libres (sin x)
del miembro izquierdo al derecho, obtenemos:
$$- \frac{21 x y}{10} - \frac{x}{10} - \frac{9 y^{2}}{5} = 9$$
Dividamos ambos miembros de la ecuación en (-9*y^2/5 - x/10 - 21*x*y/10)/x
Obtenemos la respuesta: x = -(90 + 18*y^2)/(1 + 21*y)
(9/10)*x-((7/10)*x+(3/5)*y)*3*y-x = 9
Abrimos la expresión:
- 9*y^2/5 + 9*x/10 - 21*x*y/10 - x = 9
Reducimos, obtenemos:
-9 - 9*y^2/5 - x/10 - 21*x*y/10 = 0
Transportamos los términos libres (sin x)
del miembro izquierdo al derecho, obtenemos:
$$- \frac{21 x y}{10} - \frac{x}{10} - \frac{9 y^{2}}{5} = 9$$
Dividamos ambos miembros de la ecuación en (-9*y^2/5 - x/10 - 21*x*y/10)/x
x = 9 / ((-9*y^2/5 - x/10 - 21*x*y/10)/x)
Obtenemos la respuesta: x = -(90 + 18*y^2)/(1 + 21*y)
Gráfica
Suma y producto de raíces
[src]
suma
/ / 2 2 \ \ / 2 2 \ 2 |21*\90 - 18*im (y) + 18*re (y)/*im(y) 36*(1 + 21*re(y))*im(y)*re(y)| (1 + 21*re(y))*\90 - 18*im (y) + 18*re (y)/ 756*im (y)*re(y) I*|------------------------------------- - -----------------------------| - ------------------------------------------- - ---------------------------- | 2 2 2 2 | 2 2 2 2 \ (1 + 21*re(y)) + 441*im (y) (1 + 21*re(y)) + 441*im (y)/ (1 + 21*re(y)) + 441*im (y) (1 + 21*re(y)) + 441*im (y)
$$i \left(- \frac{36 \left(21 \operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{21 \left(18 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 18 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 90\right) \operatorname{im}{\left(y\right)}}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{\left(21 \operatorname{re}{\left(y\right)} + 1\right) \left(18 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 18 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 90\right)}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{756 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}}$$
=
/ / 2 2 \ \ / 2 2 \ 2 |21*\90 - 18*im (y) + 18*re (y)/*im(y) 36*(1 + 21*re(y))*im(y)*re(y)| (1 + 21*re(y))*\90 - 18*im (y) + 18*re (y)/ 756*im (y)*re(y) I*|------------------------------------- - -----------------------------| - ------------------------------------------- - ---------------------------- | 2 2 2 2 | 2 2 2 2 \ (1 + 21*re(y)) + 441*im (y) (1 + 21*re(y)) + 441*im (y)/ (1 + 21*re(y)) + 441*im (y) (1 + 21*re(y)) + 441*im (y)
$$i \left(- \frac{36 \left(21 \operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{21 \left(18 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 18 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 90\right) \operatorname{im}{\left(y\right)}}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{\left(21 \operatorname{re}{\left(y\right)} + 1\right) \left(18 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 18 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 90\right)}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{756 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}}$$
producto
/ / 2 2 \ \ / 2 2 \ 2 |21*\90 - 18*im (y) + 18*re (y)/*im(y) 36*(1 + 21*re(y))*im(y)*re(y)| (1 + 21*re(y))*\90 - 18*im (y) + 18*re (y)/ 756*im (y)*re(y) I*|------------------------------------- - -----------------------------| - ------------------------------------------- - ---------------------------- | 2 2 2 2 | 2 2 2 2 \ (1 + 21*re(y)) + 441*im (y) (1 + 21*re(y)) + 441*im (y)/ (1 + 21*re(y)) + 441*im (y) (1 + 21*re(y)) + 441*im (y)
$$i \left(- \frac{36 \left(21 \operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{21 \left(18 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 18 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 90\right) \operatorname{im}{\left(y\right)}}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{\left(21 \operatorname{re}{\left(y\right)} + 1\right) \left(18 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 18 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 90\right)}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{756 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}}$$
=
/ / 2 2 \ 2 / 2 2 \ \
18*\- (1 + 21*re(y))*\5 + re (y) - im (y)/ - 42*im (y)*re(y) + I*\105 - 21*im (y) + 21*re (y) - 2*(1 + 21*re(y))*re(y)/*im(y)/
------------------------------------------------------------------------------------------------------------------------------
2 2
(1 + 21*re(y)) + 441*im (y)
$$\frac{18 \left(- \left(21 \operatorname{re}{\left(y\right)} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right) + i \left(- 2 \left(21 \operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 105\right) \operatorname{im}{\left(y\right)} - 42 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}}$$
18*(-(1 + 21*re(y))*(5 + re(y)^2 - im(y)^2) - 42*im(y)^2*re(y) + i*(105 - 21*im(y)^2 + 21*re(y)^2 - 2*(1 + 21*re(y))*re(y))*im(y))/((1 + 21*re(y))^2 + 441*im(y)^2)
Respuesta rápida
[src]
/ / 2 2 \ \ / 2 2 \ 2
|21*\90 - 18*im (y) + 18*re (y)/*im(y) 36*(1 + 21*re(y))*im(y)*re(y)| (1 + 21*re(y))*\90 - 18*im (y) + 18*re (y)/ 756*im (y)*re(y)
x1 = I*|------------------------------------- - -----------------------------| - ------------------------------------------- - ----------------------------
| 2 2 2 2 | 2 2 2 2
\ (1 + 21*re(y)) + 441*im (y) (1 + 21*re(y)) + 441*im (y)/ (1 + 21*re(y)) + 441*im (y) (1 + 21*re(y)) + 441*im (y)
$$x_{1} = i \left(- \frac{36 \left(21 \operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{21 \left(18 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 18 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 90\right) \operatorname{im}{\left(y\right)}}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{\left(21 \operatorname{re}{\left(y\right)} + 1\right) \left(18 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 18 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 90\right)}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{756 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(21 \operatorname{re}{\left(y\right)} + 1\right)^{2} + 441 \left(\operatorname{im}{\left(y\right)}\right)^{2}}$$
x1 = i*(-36*(21*re(y) + 1)*re(y)*im(y)/((21*re(y) + 1)^2 + 441*im(y)^2) + 21*(18*re(y)^2 - 18*im(y)^2 + 90)*im(y)/((21*re(y) + 1)^2 + 441*im(y)^2)) - (21*re(y) + 1)*(18*re(y)^2 - 18*im(y)^2 + 90)/((21*re(y) + 1)^2 + 441*im(y)^2) - 756*re(y)*im(y)^2/((21*re(y) + 1)^2 + 441*im(y)^2)