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- La ecuación:
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Ecuación x^2+5x=36
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Ecuación 3*x-6=x+4
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Ecuación 3^x=-1
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Ecuación 9^x-8*3^x-9=0
- Expresar {x} en función de y en la ecuación:
- 10*x-15*y=16
- -17*x+2*y=-4
- -2*x-19*y=3
- 6*x+17*y=-11
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Expresiones idénticas
- Ln(u)+c=- dos /(x+ uno)-Ln(x+ uno)+c
- Ln(u) más c es igual a menos 2 dividir por (x más 1) menos Ln(x más 1) más c
- Ln(u) más c es igual a menos dos dividir por (x más uno) menos Ln(x más uno) más c
- Lnu+c=-2/x+1-Lnx+1+c
- Ln(u)+c=-2 dividir por (x+1)-Ln(x+1)+c
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Expresiones semejantes
- Ln(u)+c=-2/(x+1)+Ln(x+1)+c
- Ln(u)+c=-2/(x+1)-Ln(x-1)+c
- Ln(u)+c=-2/(x+1)-Ln(x+1)-c
- Ln(u)+c=-2/(x-1)-Ln(x+1)+c
- Ln(u)+c=+2/(x+1)-Ln(x+1)+c
- Ln(u)-c=-2/(x+1)-Ln(x+1)+c
Ln(u)+c=-2/(x+1)-Ln(x+1)+c la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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2
log(u) + c = - ----- - log(x + 1) + c
x + 1
$$c + \log{\left(u \right)} = c + \left(- \log{\left(x + 1 \right)} - \frac{2}{x + 1}\right)$$
Gráfica
Respuesta rápida
[src]
// re(W(-2*u)) \ / re(W(-2*u))\ \ / re(W(-2*u)) \ / re(W(-2*u))\
|\-im(u) + e *sin(im(W(-2*u)))/*re(u) \-re(u) + cos(im(W(-2*u)))*e /*im(u)| \-im(u) + e *sin(im(W(-2*u)))/*im(u) \-re(u) + cos(im(W(-2*u)))*e /*re(u)
x1 = I*|---------------------------------------------- - ----------------------------------------------| + ---------------------------------------------- + ----------------------------------------------
| 2 2 2 2 | 2 2 2 2
\ im (u) + re (u) im (u) + re (u) / im (u) + re (u) im (u) + re (u)
$$x_{1} = \frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \sin{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{im}{\left(u\right)}\right) \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}} + \frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \cos{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{re}{\left(u\right)}\right) \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}} + i \left(\frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \sin{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{im}{\left(u\right)}\right) \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}} - \frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \cos{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{re}{\left(u\right)}\right) \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}}\right)$$
x1 = (exp(re(LambertW(-2*u)))*sin(im(LambertW(-2*u))) - im(u))*im(u)/(re(u)^2 + im(u)^2) + (exp(re(LambertW(-2*u)))*cos(im(LambertW(-2*u))) - re(u))*re(u)/(re(u)^2 + im(u)^2) + i*((exp(re(LambertW(-2*u)))*sin(im(LambertW(-2*u))) - im(u))*re(u)/(re(u)^2 + im(u)^2) - (exp(re(LambertW(-2*u)))*cos(im(LambertW(-2*u))) - re(u))*im(u)/(re(u)^2 + im(u)^2))
Suma y producto de raíces
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suma
// re(W(-2*u)) \ / re(W(-2*u))\ \ / re(W(-2*u)) \ / re(W(-2*u))\ |\-im(u) + e *sin(im(W(-2*u)))/*re(u) \-re(u) + cos(im(W(-2*u)))*e /*im(u)| \-im(u) + e *sin(im(W(-2*u)))/*im(u) \-re(u) + cos(im(W(-2*u)))*e /*re(u) I*|---------------------------------------------- - ----------------------------------------------| + ---------------------------------------------- + ---------------------------------------------- | 2 2 2 2 | 2 2 2 2 \ im (u) + re (u) im (u) + re (u) / im (u) + re (u) im (u) + re (u)
$$\frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \sin{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{im}{\left(u\right)}\right) \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}} + \frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \cos{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{re}{\left(u\right)}\right) \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}} + i \left(\frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \sin{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{im}{\left(u\right)}\right) \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}} - \frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \cos{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{re}{\left(u\right)}\right) \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}}\right)$$
=
// re(W(-2*u)) \ / re(W(-2*u))\ \ / re(W(-2*u)) \ / re(W(-2*u))\ |\-im(u) + e *sin(im(W(-2*u)))/*re(u) \-re(u) + cos(im(W(-2*u)))*e /*im(u)| \-im(u) + e *sin(im(W(-2*u)))/*im(u) \-re(u) + cos(im(W(-2*u)))*e /*re(u) I*|---------------------------------------------- - ----------------------------------------------| + ---------------------------------------------- + ---------------------------------------------- | 2 2 2 2 | 2 2 2 2 \ im (u) + re (u) im (u) + re (u) / im (u) + re (u) im (u) + re (u)
$$\frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \sin{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{im}{\left(u\right)}\right) \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}} + \frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \cos{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{re}{\left(u\right)}\right) \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}} + i \left(\frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \sin{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{im}{\left(u\right)}\right) \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}} - \frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \cos{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{re}{\left(u\right)}\right) \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}}\right)$$
producto
// re(W(-2*u)) \ / re(W(-2*u))\ \ / re(W(-2*u)) \ / re(W(-2*u))\ |\-im(u) + e *sin(im(W(-2*u)))/*re(u) \-re(u) + cos(im(W(-2*u)))*e /*im(u)| \-im(u) + e *sin(im(W(-2*u)))/*im(u) \-re(u) + cos(im(W(-2*u)))*e /*re(u) I*|---------------------------------------------- - ----------------------------------------------| + ---------------------------------------------- + ---------------------------------------------- | 2 2 2 2 | 2 2 2 2 \ im (u) + re (u) im (u) + re (u) / im (u) + re (u) im (u) + re (u)
$$\frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \sin{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{im}{\left(u\right)}\right) \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}} + \frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \cos{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{re}{\left(u\right)}\right) \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}} + i \left(\frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \sin{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{im}{\left(u\right)}\right) \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}} - \frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \cos{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{re}{\left(u\right)}\right) \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}}\right)$$
=
/ re(W(-2*u)) \ / re(W(-2*u))\ re(W(-2*u))
\-im(u) + e *sin(im(W(-2*u)))/*im(u) + \-re(u) + cos(im(W(-2*u)))*e /*re(u) + I*(re(u)*sin(im(W(-2*u))) - cos(im(W(-2*u)))*im(u))*e
------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
im (u) + re (u)
$$\frac{\left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \sin{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{im}{\left(u\right)}\right) \operatorname{im}{\left(u\right)} + \left(e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}} \cos{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} - \operatorname{re}{\left(u\right)}\right) \operatorname{re}{\left(u\right)} + i \left(\sin{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} \operatorname{re}{\left(u\right)} - \cos{\left(\operatorname{im}{\left(W\left(- 2 u\right)\right)} \right)} \operatorname{im}{\left(u\right)}\right) e^{\operatorname{re}{\left(W\left(- 2 u\right)\right)}}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} + \left(\operatorname{im}{\left(u\right)}\right)^{2}}$$
((-im(u) + exp(re(LambertW(-2*u)))*sin(im(LambertW(-2*u))))*im(u) + (-re(u) + cos(im(LambertW(-2*u)))*exp(re(LambertW(-2*u))))*re(u) + i*(re(u)*sin(im(LambertW(-2*u))) - cos(im(LambertW(-2*u)))*im(u))*exp(re(LambertW(-2*u))))/(im(u)^2 + re(u)^2)