Sr Examen
Otras calculadoras
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- La ecuación:
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Ecuación x^3
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Ecuación x+357=642
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Ecuación 4*x-4=12
-
Ecuación 3x+1=-2
- Expresar {x} en función de y en la ecuación:
- 9*x+7*y=4
- 2*x+5*y=1
- -1*x+11*y=16
- -3*x-9*y=16
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Expresiones idénticas
- x- tres /(c- cuatro)²= dos , cuatro / dieciséis -c²
- x menos 3 dividir por (c menos 4)² es igual a 2,4 dividir por 16 menos c²
- x menos tres dividir por (c menos cuatro)² es igual a dos , cuatro dividir por dieciséis menos c²
- x-3/c-4²=2,4/16-c²
- x-3 dividir por (c-4)²=2,4 dividir por 16-c²
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Expresiones semejantes
- x-3/(c-4)²=2,4/16+c²
- x+3/(c-4)²=2,4/16-c²
- x-3/(c+4)²=2,4/16-c²
x-3/(c-4)²=2,4/16-c² la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 12 2
x - -------- = ---- - c
2 5*16
(c - 4)
$$x - \frac{3}{\left(c - 4\right)^{2}} = - c^{2} + \frac{12}{5 \cdot 16}$$
Solución detallada
Tenemos la ecuación:
$$x - \frac{3}{\left(c - 4\right)^{2}} = - c^{2} + \frac{12}{5 \cdot 16}$$
cambiamos:
$$x - \frac{3}{\left(c - 4\right)^{2}} = \frac{3}{20} - c^{2}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
Transportamos los términos libres (sin x)
del miembro izquierdo al derecho, obtenemos:
$$x + 4 - \frac{3}{\left(c - 4\right)^{2}} = \frac{83}{20} - c^{2}$$
Dividamos ambos miembros de la ecuación en (4 + x - 3/(-4 + c)^2)/x
Obtenemos la respuesta: x = 3/20 - c^2 + 3/(-4 + c)^2
$$x - \frac{3}{\left(c - 4\right)^{2}} = - c^{2} + \frac{12}{5 \cdot 16}$$
cambiamos:
$$x - \frac{3}{\left(c - 4\right)^{2}} = \frac{3}{20} - c^{2}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
x - -3/4+3/c^2 = 3/20 - c^2
Transportamos los términos libres (sin x)
del miembro izquierdo al derecho, obtenemos:
$$x + 4 - \frac{3}{\left(c - 4\right)^{2}} = \frac{83}{20} - c^{2}$$
Dividamos ambos miembros de la ecuación en (4 + x - 3/(-4 + c)^2)/x
x = 83/20 - c^2 / ((4 + x - 3/(-4 + c)^2)/x)
Obtenemos la respuesta: x = 3/20 - c^2 + 3/(-4 + c)^2
Gráfica
Suma y producto de raíces
[src]
suma
2 2
3 2 2 / 6*(-4 + re(c))*im(c) \ 3*im (c) 3*(-4 + re(c))
-- + im (c) - re (c) + I*|-2*im(c)*re(c) - -------------------------| - ------------------------- + -------------------------
20 | 2| 2 2
| / 2 2 \ | / 2 2 \ / 2 2 \
\ \(-4 + re(c)) + im (c)/ / \(-4 + re(c)) + im (c)/ \(-4 + re(c)) + im (c)/
$$i \left(- 2 \operatorname{re}{\left(c\right)} \operatorname{im}{\left(c\right)} - \frac{6 \left(\operatorname{re}{\left(c\right)} - 4\right) \operatorname{im}{\left(c\right)}}{\left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}\right) - \left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2} + \frac{3}{20} + \frac{3 \left(\operatorname{re}{\left(c\right)} - 4\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}} - \frac{3 \left(\operatorname{im}{\left(c\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}$$
=
2 2
3 2 2 / 6*(-4 + re(c))*im(c) \ 3*im (c) 3*(-4 + re(c))
-- + im (c) - re (c) + I*|-2*im(c)*re(c) - -------------------------| - ------------------------- + -------------------------
20 | 2| 2 2
| / 2 2 \ | / 2 2 \ / 2 2 \
\ \(-4 + re(c)) + im (c)/ / \(-4 + re(c)) + im (c)/ \(-4 + re(c)) + im (c)/
$$i \left(- 2 \operatorname{re}{\left(c\right)} \operatorname{im}{\left(c\right)} - \frac{6 \left(\operatorname{re}{\left(c\right)} - 4\right) \operatorname{im}{\left(c\right)}}{\left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}\right) - \left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2} + \frac{3}{20} + \frac{3 \left(\operatorname{re}{\left(c\right)} - 4\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}} - \frac{3 \left(\operatorname{im}{\left(c\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}$$
producto
2 2
3 2 2 / 6*(-4 + re(c))*im(c) \ 3*im (c) 3*(-4 + re(c))
-- + im (c) - re (c) + I*|-2*im(c)*re(c) - -------------------------| - ------------------------- + -------------------------
20 | 2| 2 2
| / 2 2 \ | / 2 2 \ / 2 2 \
\ \(-4 + re(c)) + im (c)/ / \(-4 + re(c)) + im (c)/ \(-4 + re(c)) + im (c)/
$$i \left(- 2 \operatorname{re}{\left(c\right)} \operatorname{im}{\left(c\right)} - \frac{6 \left(\operatorname{re}{\left(c\right)} - 4\right) \operatorname{im}{\left(c\right)}}{\left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}\right) - \left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2} + \frac{3}{20} + \frac{3 \left(\operatorname{re}{\left(c\right)} - 4\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}} - \frac{3 \left(\operatorname{im}{\left(c\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}$$
=
2 / 2 \
2 2 / 2 2 \ / 2 2 \ | / 2 2 \ |
- 60*im (c) + 60*(-4 + re(c)) + \(-4 + re(c)) + im (c)/ *\3 - 20*re (c) + 20*im (c)/ + 40*I*\12 - 3*re(c) - \(-4 + re(c)) + im (c)/ *re(c)/*im(c)
----------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2 2 \
20*\(-4 + re(c)) + im (c)/
$$\frac{\left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2} \left(- 20 \left(\operatorname{re}{\left(c\right)}\right)^{2} + 20 \left(\operatorname{im}{\left(c\right)}\right)^{2} + 3\right) + 60 \left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + 40 i \left(- \left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2} \operatorname{re}{\left(c\right)} - 3 \operatorname{re}{\left(c\right)} + 12\right) \operatorname{im}{\left(c\right)} - 60 \left(\operatorname{im}{\left(c\right)}\right)^{2}}{20 \left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}$$
(-60*im(c)^2 + 60*(-4 + re(c))^2 + ((-4 + re(c))^2 + im(c)^2)^2*(3 - 20*re(c)^2 + 20*im(c)^2) + 40*i*(12 - 3*re(c) - ((-4 + re(c))^2 + im(c)^2)^2*re(c))*im(c))/(20*((-4 + re(c))^2 + im(c)^2)^2)
Respuesta rápida
[src]
2 2
3 2 2 / 6*(-4 + re(c))*im(c) \ 3*im (c) 3*(-4 + re(c))
x1 = -- + im (c) - re (c) + I*|-2*im(c)*re(c) - -------------------------| - ------------------------- + -------------------------
20 | 2| 2 2
| / 2 2 \ | / 2 2 \ / 2 2 \
\ \(-4 + re(c)) + im (c)/ / \(-4 + re(c)) + im (c)/ \(-4 + re(c)) + im (c)/
$$x_{1} = i \left(- 2 \operatorname{re}{\left(c\right)} \operatorname{im}{\left(c\right)} - \frac{6 \left(\operatorname{re}{\left(c\right)} - 4\right) \operatorname{im}{\left(c\right)}}{\left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}\right) - \left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2} + \frac{3}{20} + \frac{3 \left(\operatorname{re}{\left(c\right)} - 4\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}} - \frac{3 \left(\operatorname{im}{\left(c\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)} - 4\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}$$
x1 = i*(-2*re(c)*im(c) - 6*(re(c) - 4)*im(c)/((re(c) - 4)^2 + im(c)^2)^2) - re(c)^2 + im(c)^2 + 3/20 + 3*(re(c) - 4)^2/((re(c) - 4)^2 + im(c)^2)^2 - 3*im(c)^2/((re(c) - 4)^2 + im(c)^2)^2