Sr Examen

Otras calculadoras

u=arctg((x+y)/(1-xy)) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
        / x + y \
u = atan|-------|
        \1 - x*y/
u=atan⁡(x+y−xy+1)u = \operatorname{atan}{\left(\frac{x + y}{- x y + 1} \right)}
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
  /                   /                sinh(2*im(u))        \   /                 sin(2*re(u))        \             \                      /                 sin(2*re(u))        \   /                sinh(2*im(u))        \             
  |(1 + re(x*tan(u)))*|-im(x) + ----------------------------|   |-re(x) + ----------------------------|*im(x*tan(u))|   (1 + re(x*tan(u)))*|-re(x) + ----------------------------|   |-im(x) + ----------------------------|*im(x*tan(u))
  |                   \         cos(2*re(u)) + cosh(2*im(u))/   \         cos(2*re(u)) + cosh(2*im(u))/             |                      \         cos(2*re(u)) + cosh(2*im(u))/   \         cos(2*re(u)) + cosh(2*im(u))/             
I*|---------------------------------------------------------- - ----------------------------------------------------| + ---------------------------------------------------------- + ----------------------------------------------------
  |                             2     2                                                   2     2                   |                                2     2                                                   2     2                   
  \           (1 + re(x*tan(u)))  + im (x*tan(u))                       (1 + re(x*tan(u)))  + im (x*tan(u))         /              (1 + re(x*tan(u)))  + im (x*tan(u))                       (1 + re(x*tan(u)))  + im (x*tan(u))
i(−(−re⁡(x)+sin⁡(2re⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))im⁡(xtan⁡(u))(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2+(re⁡(xtan⁡(u))+1)(−im⁡(x)+sinh⁡(2im⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2)+(−re⁡(x)+sin⁡(2re⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))(re⁡(xtan⁡(u))+1)(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2+(−im⁡(x)+sinh⁡(2im⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))im⁡(xtan⁡(u))(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2i \left(- \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right) \left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} 
=
  /                   /                sinh(2*im(u))        \   /                 sin(2*re(u))        \             \                      /                 sin(2*re(u))        \   /                sinh(2*im(u))        \             
  |(1 + re(x*tan(u)))*|-im(x) + ----------------------------|   |-re(x) + ----------------------------|*im(x*tan(u))|   (1 + re(x*tan(u)))*|-re(x) + ----------------------------|   |-im(x) + ----------------------------|*im(x*tan(u))
  |                   \         cos(2*re(u)) + cosh(2*im(u))/   \         cos(2*re(u)) + cosh(2*im(u))/             |                      \         cos(2*re(u)) + cosh(2*im(u))/   \         cos(2*re(u)) + cosh(2*im(u))/             
I*|---------------------------------------------------------- - ----------------------------------------------------| + ---------------------------------------------------------- + ----------------------------------------------------
  |                             2     2                                                   2     2                   |                                2     2                                                   2     2                   
  \           (1 + re(x*tan(u)))  + im (x*tan(u))                       (1 + re(x*tan(u)))  + im (x*tan(u))         /              (1 + re(x*tan(u)))  + im (x*tan(u))                       (1 + re(x*tan(u)))  + im (x*tan(u))
i(−(−re⁡(x)+sin⁡(2re⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))im⁡(xtan⁡(u))(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2+(re⁡(xtan⁡(u))+1)(−im⁡(x)+sinh⁡(2im⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2)+(−re⁡(x)+sin⁡(2re⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))(re⁡(xtan⁡(u))+1)(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2+(−im⁡(x)+sinh⁡(2im⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))im⁡(xtan⁡(u))(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2i \left(- \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right) \left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} 
producto
  /                   /                sinh(2*im(u))        \   /                 sin(2*re(u))        \             \                      /                 sin(2*re(u))        \   /                sinh(2*im(u))        \             
  |(1 + re(x*tan(u)))*|-im(x) + ----------------------------|   |-re(x) + ----------------------------|*im(x*tan(u))|   (1 + re(x*tan(u)))*|-re(x) + ----------------------------|   |-im(x) + ----------------------------|*im(x*tan(u))
  |                   \         cos(2*re(u)) + cosh(2*im(u))/   \         cos(2*re(u)) + cosh(2*im(u))/             |                      \         cos(2*re(u)) + cosh(2*im(u))/   \         cos(2*re(u)) + cosh(2*im(u))/             
I*|---------------------------------------------------------- - ----------------------------------------------------| + ---------------------------------------------------------- + ----------------------------------------------------
  |                             2     2                                                   2     2                   |                                2     2                                                   2     2                   
  \           (1 + re(x*tan(u)))  + im (x*tan(u))                       (1 + re(x*tan(u)))  + im (x*tan(u))         /              (1 + re(x*tan(u)))  + im (x*tan(u))                       (1 + re(x*tan(u)))  + im (x*tan(u))
i(−(−re⁡(x)+sin⁡(2re⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))im⁡(xtan⁡(u))(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2+(re⁡(xtan⁡(u))+1)(−im⁡(x)+sinh⁡(2im⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2)+(−re⁡(x)+sin⁡(2re⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))(re⁡(xtan⁡(u))+1)(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2+(−im⁡(x)+sinh⁡(2im⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))im⁡(xtan⁡(u))(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2i \left(- \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right) \left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} 
=
-((1 + re(x*tan(u)))*(-sin(2*re(u)) + (cos(2*re(u)) + cosh(2*im(u)))*re(x)) + (-sinh(2*im(u)) + (cos(2*re(u)) + cosh(2*im(u)))*im(x))*im(x*tan(u)) - I*((-sin(2*re(u)) + (cos(2*re(u)) + cosh(2*im(u)))*re(x))*im(x*tan(u)) - (1 + re(x*tan(u)))*(-sinh(2*im(u)) + (cos(2*re(u)) + cosh(2*im(u)))*im(x)))) 
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                    /                  2     2          \                                                                                                                                                  
                                                                                                                    \(1 + re(x*tan(u)))  + im (x*tan(u))/*(cos(2*re(u)) + cosh(2*im(u)))
−−i(((cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))re⁡(x)−sin⁡(2re⁡(u)))im⁡(xtan⁡(u))−((cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))im⁡(x)−sinh⁡(2im⁡(u)))(re⁡(xtan⁡(u))+1))+((cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))re⁡(x)−sin⁡(2re⁡(u)))(re⁡(xtan⁡(u))+1)+((cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))im⁡(x)−sinh⁡(2im⁡(u)))im⁡(xtan⁡(u))((re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2)(cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))- \frac{- i \left(\left(\left(\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right) \operatorname{re}{\left(x\right)} - \sin{\left(2 \operatorname{re}{\left(u\right)} \right)}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)} - \left(\left(\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right) \operatorname{im}{\left(x\right)} - \sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right) \left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)\right) + \left(\left(\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right) \operatorname{re}{\left(x\right)} - \sin{\left(2 \operatorname{re}{\left(u\right)} \right)}\right) \left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right) + \left(\left(\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right) \operatorname{im}{\left(x\right)} - \sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}\right) \left(\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}\right)} 
-((1 + re(x*tan(u)))*(-sin(2*re(u)) + (cos(2*re(u)) + cosh(2*im(u)))*re(x)) + (-sinh(2*im(u)) + (cos(2*re(u)) + cosh(2*im(u)))*im(x))*im(x*tan(u)) - i*((-sin(2*re(u)) + (cos(2*re(u)) + cosh(2*im(u)))*re(x))*im(x*tan(u)) - (1 + re(x*tan(u)))*(-sinh(2*im(u)) + (cos(2*re(u)) + cosh(2*im(u)))*im(x))))/(((1 + re(x*tan(u)))^2 + im(x*tan(u))^2)*(cos(2*re(u)) + cosh(2*im(u))))
Respuesta rápida [src] 
       /                   /                sinh(2*im(u))        \   /                 sin(2*re(u))        \             \                      /                 sin(2*re(u))        \   /                sinh(2*im(u))        \             
       |(1 + re(x*tan(u)))*|-im(x) + ----------------------------|   |-re(x) + ----------------------------|*im(x*tan(u))|   (1 + re(x*tan(u)))*|-re(x) + ----------------------------|   |-im(x) + ----------------------------|*im(x*tan(u))
       |                   \         cos(2*re(u)) + cosh(2*im(u))/   \         cos(2*re(u)) + cosh(2*im(u))/             |                      \         cos(2*re(u)) + cosh(2*im(u))/   \         cos(2*re(u)) + cosh(2*im(u))/             
y1 = I*|---------------------------------------------------------- - ----------------------------------------------------| + ---------------------------------------------------------- + ----------------------------------------------------
       |                             2     2                                                   2     2                   |                                2     2                                                   2     2                   
       \           (1 + re(x*tan(u)))  + im (x*tan(u))                       (1 + re(x*tan(u)))  + im (x*tan(u))         /              (1 + re(x*tan(u)))  + im (x*tan(u))                       (1 + re(x*tan(u)))  + im (x*tan(u))
y1=i(−(−re⁡(x)+sin⁡(2re⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))im⁡(xtan⁡(u))(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2+(re⁡(xtan⁡(u))+1)(−im⁡(x)+sinh⁡(2im⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2)+(−re⁡(x)+sin⁡(2re⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))(re⁡(xtan⁡(u))+1)(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2+(−im⁡(x)+sinh⁡(2im⁡(u))cos⁡(2re⁡(u))+cosh⁡(2im⁡(u)))im⁡(xtan⁡(u))(re⁡(xtan⁡(u))+1)2+(im⁡(xtan⁡(u)))2y_{1} = i \left(- \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right) \left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(x\right)} + \frac{\sin{\left(2 \operatorname{re}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(x\right)} + \frac{\sinh{\left(2 \operatorname{im}{\left(u\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(u\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(u\right)} \right)}}\right) \operatorname{im}{\left(x \tan{\left(u \right)}\right)}}{\left(\operatorname{re}{\left(x \tan{\left(u \right)}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x \tan{\left(u \right)}\right)}\right)^{2}} 
y1 = i*(-(-re(x) + sin(2*re(u))/(cos(2*re(u)) + cosh(2*im(u))))*im(x*tan(u))/((re(x*tan(u)) + 1)^2 + im(x*tan(u))^2) + (re(x*tan(u)) + 1)*(-im(x) + sinh(2*im(u))/(cos(2*re(u)) + cosh(2*im(u))))/((re(x*tan(u)) + 1)^2 + im(x*tan(u))^2)) + (-re(x) + sin(2*re(u))/(cos(2*re(u)) + cosh(2*im(u))))*(re(x*tan(u)) + 1)/((re(x*tan(u)) + 1)^2 + im(x*tan(u))^2) + (-im(x) + sinh(2*im(u))/(cos(2*re(u)) + cosh(2*im(u))))*im(x*tan(u))/((re(x*tan(u)) + 1)^2 + im(x*tan(u))^2)
    © Sr Examen – Калькулятор