Sr Examen

Otras calculadoras

yx-y=-1 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] 
y*x - y = -1
xy−y=−1x y - y = -1
Simplificar
Solución detallada
Tenemos una ecuación lineal:
y*x-y = -1

Dividamos ambos miembros de la ecuación en (-y + x*y)/x
x = -1 / ((-y + x*y)/x)

Obtenemos la respuesta: x = (-1 + y)/y
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
xy−y=−1x y - y = -1
Коэффициент при x равен
yy
entonces son posibles los casos para y :
y<0y < 0
y=0y = 0
Consideremos todos los casos con detalles:
Con
y<0y < 0
la ecuación será
2−x=02 - x = 0
su solución
x=2x = 2
Con
y=0y = 0
la ecuación será
1=01 = 0
su solución
no hay soluciones
Gráfica
Respuesta rápida [src] 
                                                       2                            
       /  im(y)*re(y)     (-1 + re(y))*im(y)\        im (y)       (-1 + re(y))*re(y)
x1 = I*|--------------- - ------------------| + --------------- + ------------------
       |  2        2         2        2     |     2        2         2        2     
       \im (y) + re (y)    im (y) + re (y)  /   im (y) + re (y)    im (y) + re (y)
x1=i(−(re⁡(y)−1)im⁡(y)(re⁡(y))2+(im⁡(y))2+re⁡(y)im⁡(y)(re⁡(y))2+(im⁡(y))2)+(re⁡(y)−1)re⁡(y)(re⁡(y))2+(im⁡(y))2+(im⁡(y))2(re⁡(y))2+(im⁡(y))2x_{1} = i \left(- \frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
x1 = i*(-(re(y) - 1)*im(y)/(re(y)^2 + im(y)^2) + re(y)*im(y)/(re(y)^2 + im(y)^2)) + (re(y) - 1)*re(y)/(re(y)^2 + im(y)^2) + im(y)^2/(re(y)^2 + im(y)^2)
Suma y producto de raíces [src] 
suma
                                                  2                            
  /  im(y)*re(y)     (-1 + re(y))*im(y)\        im (y)       (-1 + re(y))*re(y)
I*|--------------- - ------------------| + --------------- + ------------------
  |  2        2         2        2     |     2        2         2        2     
  \im (y) + re (y)    im (y) + re (y)  /   im (y) + re (y)    im (y) + re (y)
i(−(re⁡(y)−1)im⁡(y)(re⁡(y))2+(im⁡(y))2+re⁡(y)im⁡(y)(re⁡(y))2+(im⁡(y))2)+(re⁡(y)−1)re⁡(y)(re⁡(y))2+(im⁡(y))2+(im⁡(y))2(re⁡(y))2+(im⁡(y))2i \left(- \frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
=
                                                  2                            
  /  im(y)*re(y)     (-1 + re(y))*im(y)\        im (y)       (-1 + re(y))*re(y)
I*|--------------- - ------------------| + --------------- + ------------------
  |  2        2         2        2     |     2        2         2        2     
  \im (y) + re (y)    im (y) + re (y)  /   im (y) + re (y)    im (y) + re (y)
i(−(re⁡(y)−1)im⁡(y)(re⁡(y))2+(im⁡(y))2+re⁡(y)im⁡(y)(re⁡(y))2+(im⁡(y))2)+(re⁡(y)−1)re⁡(y)(re⁡(y))2+(im⁡(y))2+(im⁡(y))2(re⁡(y))2+(im⁡(y))2i \left(- \frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
producto
                                                  2                            
  /  im(y)*re(y)     (-1 + re(y))*im(y)\        im (y)       (-1 + re(y))*re(y)
I*|--------------- - ------------------| + --------------- + ------------------
  |  2        2         2        2     |     2        2         2        2     
  \im (y) + re (y)    im (y) + re (y)  /   im (y) + re (y)    im (y) + re (y)
i(−(re⁡(y)−1)im⁡(y)(re⁡(y))2+(im⁡(y))2+re⁡(y)im⁡(y)(re⁡(y))2+(im⁡(y))2)+(re⁡(y)−1)re⁡(y)(re⁡(y))2+(im⁡(y))2+(im⁡(y))2(re⁡(y))2+(im⁡(y))2i \left(- \frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
=
  2                                  
im (y) + I*im(y) + (-1 + re(y))*re(y)
-------------------------------------
             2        2              
           im (y) + re (y)
(re⁡(y)−1)re⁡(y)+(im⁡(y))2+iim⁡(y)(re⁡(y))2+(im⁡(y))2\frac{\left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + i \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
(im(y)^2 + i*im(y) + (-1 + re(y))*re(y))/(im(y)^2 + re(y)^2)
    © Sr Examen – Калькулятор