Sr Examen

Otras calculadoras

ax+b=c 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] 
a*x + b = c
ax+b=ca x + b = c
Simplificar
Solución detallada
Tenemos una ecuación lineal:
a*x+b = c

Dividamos ambos miembros de la ecuación en (b + a*x)/x
x = c / ((b + a*x)/x)

Obtenemos la respuesta: x = (c - b)/a
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
ax+b=ca x + b = c
Коэффициент при x равен
aa
entonces son posibles los casos para a :
a<0a < 0
a=0a = 0
Consideremos todos los casos con detalles:
Con
a<0a < 0
la ecuación será
b−c−x=0b - c - x = 0
su solución
x=b−cx = b - c
Con
a=0a = 0
la ecuación será
b−c=0b - c = 0
su solución
Gráfica
Respuesta rápida [src] 
       /(-im(b) + im(c))*re(a)   (-re(b) + re(c))*im(a)\   (-im(b) + im(c))*im(a)   (-re(b) + re(c))*re(a)
x1 = I*|---------------------- - ----------------------| + ---------------------- + ----------------------
       |     2        2               2        2       |        2        2               2        2       
       \   im (a) + re (a)          im (a) + re (a)    /      im (a) + re (a)          im (a) + re (a)
x1=i(−(−re⁡(b)+re⁡(c))im⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(b)+im⁡(c))re⁡(a)(re⁡(a))2+(im⁡(a))2)+(−re⁡(b)+re⁡(c))re⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(b)+im⁡(c))im⁡(a)(re⁡(a))2+(im⁡(a))2x_{1} = i \left(- \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} 
x1 = i*(-(-re(b) + re(c))*im(a)/(re(a)^2 + im(a)^2) + (-im(b) + im(c))*re(a)/(re(a)^2 + im(a)^2)) + (-re(b) + re(c))*re(a)/(re(a)^2 + im(a)^2) + (-im(b) + im(c))*im(a)/(re(a)^2 + im(a)^2)
Suma y producto de raíces [src] 
suma
  /(-im(b) + im(c))*re(a)   (-re(b) + re(c))*im(a)\   (-im(b) + im(c))*im(a)   (-re(b) + re(c))*re(a)
I*|---------------------- - ----------------------| + ---------------------- + ----------------------
  |     2        2               2        2       |        2        2               2        2       
  \   im (a) + re (a)          im (a) + re (a)    /      im (a) + re (a)          im (a) + re (a)
i(−(−re⁡(b)+re⁡(c))im⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(b)+im⁡(c))re⁡(a)(re⁡(a))2+(im⁡(a))2)+(−re⁡(b)+re⁡(c))re⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(b)+im⁡(c))im⁡(a)(re⁡(a))2+(im⁡(a))2i \left(- \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} 
=
  /(-im(b) + im(c))*re(a)   (-re(b) + re(c))*im(a)\   (-im(b) + im(c))*im(a)   (-re(b) + re(c))*re(a)
I*|---------------------- - ----------------------| + ---------------------- + ----------------------
  |     2        2               2        2       |        2        2               2        2       
  \   im (a) + re (a)          im (a) + re (a)    /      im (a) + re (a)          im (a) + re (a)
i(−(−re⁡(b)+re⁡(c))im⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(b)+im⁡(c))re⁡(a)(re⁡(a))2+(im⁡(a))2)+(−re⁡(b)+re⁡(c))re⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(b)+im⁡(c))im⁡(a)(re⁡(a))2+(im⁡(a))2i \left(- \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} 
producto
  /(-im(b) + im(c))*re(a)   (-re(b) + re(c))*im(a)\   (-im(b) + im(c))*im(a)   (-re(b) + re(c))*re(a)
I*|---------------------- - ----------------------| + ---------------------- + ----------------------
  |     2        2               2        2       |        2        2               2        2       
  \   im (a) + re (a)          im (a) + re (a)    /      im (a) + re (a)          im (a) + re (a)
i(−(−re⁡(b)+re⁡(c))im⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(b)+im⁡(c))re⁡(a)(re⁡(a))2+(im⁡(a))2)+(−re⁡(b)+re⁡(c))re⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(b)+im⁡(c))im⁡(a)(re⁡(a))2+(im⁡(a))2i \left(- \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} 
=
I*((-re(c) + re(b))*im(a) - (-im(c) + im(b))*re(a)) - (-im(c) + im(b))*im(a) - (-re(c) + re(b))*re(a)
-----------------------------------------------------------------------------------------------------
                                             2        2                                              
                                           im (a) + re (a)
i((re⁡(b)−re⁡(c))im⁡(a)−(im⁡(b)−im⁡(c))re⁡(a))−(re⁡(b)−re⁡(c))re⁡(a)−(im⁡(b)−im⁡(c))im⁡(a)(re⁡(a))2+(im⁡(a))2\frac{i \left(\left(\operatorname{re}{\left(b\right)} - \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)} - \left(\operatorname{im}{\left(b\right)} - \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}\right) - \left(\operatorname{re}{\left(b\right)} - \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(b\right)} - \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} 
(i*((-re(c) + re(b))*im(a) - (-im(c) + im(b))*re(a)) - (-im(c) + im(b))*im(a) - (-re(c) + re(b))*re(a))/(im(a)^2 + re(a)^2)
    © Sr Examen – Калькулятор