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sqrt(2*a*y*(b+a)-a^(2))-c-a=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
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\/  2*a*y*(b + a) - a   - c - a = 0
−a+(−c+−a2+2ay(a+b))=0- a + \left(- c + \sqrt{- a^{2} + 2 a y \left(a + b\right)}\right) = 0
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Gráfica
Respuesta rápida [src] 
       /                                                      /    1    \   /               2     2                     2     2   \   /    1    \\   /               2     2                     2     2   \   /    1    \                                                         /    1    \
       |(2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*re|---------|   \(re(a) + re(c))  + re (a) - (im(a) + im(c))  - im (a)/*im|---------||   \(re(a) + re(c))  + re (a) - (im(a) + im(c))  - im (a)/*re|---------|   (2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*im|---------|
       |                                                      \a*(a + b)/                                                             \a*(a + b)/|                                                             \a*(a + b)/                                                         \a*(a + b)/
y1 = I*|----------------------------------------------------------------- + ---------------------------------------------------------------------| + --------------------------------------------------------------------- - -----------------------------------------------------------------
       \                                2                                                                     2                                  /                                     2                                                                     2
y1=i((2(re⁡(a)+re⁡(c))(im⁡(a)+im⁡(c))+2re⁡(a)im⁡(a))re⁡(1a(a+b))2+((re⁡(a)+re⁡(c))2−(im⁡(a)+im⁡(c))2+(re⁡(a))2−(im⁡(a))2)im⁡(1a(a+b))2)−(2(re⁡(a)+re⁡(c))(im⁡(a)+im⁡(c))+2re⁡(a)im⁡(a))im⁡(1a(a+b))2+((re⁡(a)+re⁡(c))2−(im⁡(a)+im⁡(c))2+(re⁡(a))2−(im⁡(a))2)re⁡(1a(a+b))2y_{1} = i \left(\frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}\right) - \frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} 
y1 = i*((2*(re(a) + re(c))*(im(a) + im(c)) + 2*re(a)*im(a))*re(1/(a*(a + b)))/2 + ((re(a) + re(c))^2 - (im(a) + im(c))^2 + re(a)^2 - im(a)^2)*im(1/(a*(a + b)))/2) - (2*(re(a) + re(c))*(im(a) + im(c)) + 2*re(a)*im(a))*im(1/(a*(a + b)))/2 + ((re(a) + re(c))^2 - (im(a) + im(c))^2 + re(a)^2 - im(a)^2)*re(1/(a*(a + b)))/2
Suma y producto de raíces [src] 
suma
  /                                                      /    1    \   /               2     2                     2     2   \   /    1    \\   /               2     2                     2     2   \   /    1    \                                                         /    1    \
  |(2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*re|---------|   \(re(a) + re(c))  + re (a) - (im(a) + im(c))  - im (a)/*im|---------||   \(re(a) + re(c))  + re (a) - (im(a) + im(c))  - im (a)/*re|---------|   (2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*im|---------|
  |                                                      \a*(a + b)/                                                             \a*(a + b)/|                                                             \a*(a + b)/                                                         \a*(a + b)/
I*|----------------------------------------------------------------- + ---------------------------------------------------------------------| + --------------------------------------------------------------------- - -----------------------------------------------------------------
  \                                2                                                                     2                                  /                                     2                                                                     2
i((2(re⁡(a)+re⁡(c))(im⁡(a)+im⁡(c))+2re⁡(a)im⁡(a))re⁡(1a(a+b))2+((re⁡(a)+re⁡(c))2−(im⁡(a)+im⁡(c))2+(re⁡(a))2−(im⁡(a))2)im⁡(1a(a+b))2)−(2(re⁡(a)+re⁡(c))(im⁡(a)+im⁡(c))+2re⁡(a)im⁡(a))im⁡(1a(a+b))2+((re⁡(a)+re⁡(c))2−(im⁡(a)+im⁡(c))2+(re⁡(a))2−(im⁡(a))2)re⁡(1a(a+b))2i \left(\frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}\right) - \frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} 
=
  /                                                      /    1    \   /               2     2                     2     2   \   /    1    \\   /               2     2                     2     2   \   /    1    \                                                         /    1    \
  |(2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*re|---------|   \(re(a) + re(c))  + re (a) - (im(a) + im(c))  - im (a)/*im|---------||   \(re(a) + re(c))  + re (a) - (im(a) + im(c))  - im (a)/*re|---------|   (2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*im|---------|
  |                                                      \a*(a + b)/                                                             \a*(a + b)/|                                                             \a*(a + b)/                                                         \a*(a + b)/
I*|----------------------------------------------------------------- + ---------------------------------------------------------------------| + --------------------------------------------------------------------- - -----------------------------------------------------------------
  \                                2                                                                     2                                  /                                     2                                                                     2
i((2(re⁡(a)+re⁡(c))(im⁡(a)+im⁡(c))+2re⁡(a)im⁡(a))re⁡(1a(a+b))2+((re⁡(a)+re⁡(c))2−(im⁡(a)+im⁡(c))2+(re⁡(a))2−(im⁡(a))2)im⁡(1a(a+b))2)−(2(re⁡(a)+re⁡(c))(im⁡(a)+im⁡(c))+2re⁡(a)im⁡(a))im⁡(1a(a+b))2+((re⁡(a)+re⁡(c))2−(im⁡(a)+im⁡(c))2+(re⁡(a))2−(im⁡(a))2)re⁡(1a(a+b))2i \left(\frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}\right) - \frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} 
producto
  /                                                      /    1    \   /               2     2                     2     2   \   /    1    \\   /               2     2                     2     2   \   /    1    \                                                         /    1    \
  |(2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*re|---------|   \(re(a) + re(c))  + re (a) - (im(a) + im(c))  - im (a)/*im|---------||   \(re(a) + re(c))  + re (a) - (im(a) + im(c))  - im (a)/*re|---------|   (2*(im(a) + im(c))*(re(a) + re(c)) + 2*im(a)*re(a))*im|---------|
  |                                                      \a*(a + b)/                                                             \a*(a + b)/|                                                             \a*(a + b)/                                                         \a*(a + b)/
I*|----------------------------------------------------------------- + ---------------------------------------------------------------------| + --------------------------------------------------------------------- - -----------------------------------------------------------------
  \                                2                                                                     2                                  /                                     2                                                                     2
i((2(re⁡(a)+re⁡(c))(im⁡(a)+im⁡(c))+2re⁡(a)im⁡(a))re⁡(1a(a+b))2+((re⁡(a)+re⁡(c))2−(im⁡(a)+im⁡(c))2+(re⁡(a))2−(im⁡(a))2)im⁡(1a(a+b))2)−(2(re⁡(a)+re⁡(c))(im⁡(a)+im⁡(c))+2re⁡(a)im⁡(a))im⁡(1a(a+b))2+((re⁡(a)+re⁡(c))2−(im⁡(a)+im⁡(c))2+(re⁡(a))2−(im⁡(a))2)re⁡(1a(a+b))2i \left(\frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}\right) - \frac{\left(2 \left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} 
=
  /                                                                /               2     2                     2     2   \   /    1    \\   /               2     2                     2     2   \   /    1    \                                                                
  |                                                                \(re(a) + re(c))  + re (a) - (im(a) + im(c))  - im (a)/*im|---------||   \(re(a) + re(c))  + re (a) - (im(a) + im(c))  - im (a)/*re|---------|                                                                
  |                                                  /    1    \                                                             \a*(a + b)/|                                                             \a*(a + b)/                                                     /    1    \
I*|((im(a) + im(c))*(re(a) + re(c)) + im(a)*re(a))*re|---------| + ---------------------------------------------------------------------| + --------------------------------------------------------------------- - ((im(a) + im(c))*(re(a) + re(c)) + im(a)*re(a))*im|---------|
  \                                                  \a*(a + b)/                                     2                                  /                                     2                                                                                       \a*(a + b)/
i(((re⁡(a)+re⁡(c))(im⁡(a)+im⁡(c))+re⁡(a)im⁡(a))re⁡(1a(a+b))+((re⁡(a)+re⁡(c))2−(im⁡(a)+im⁡(c))2+(re⁡(a))2−(im⁡(a))2)im⁡(1a(a+b))2)−((re⁡(a)+re⁡(c))(im⁡(a)+im⁡(c))+re⁡(a)im⁡(a))im⁡(1a(a+b))+((re⁡(a)+re⁡(c))2−(im⁡(a)+im⁡(c))2+(re⁡(a))2−(im⁡(a))2)re⁡(1a(a+b))2i \left(\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2}\right) - \left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(\frac{1}{a \left(a + b\right)}\right)} + \frac{\left(\left(\operatorname{re}{\left(a\right)} + \operatorname{re}{\left(c\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a \left(a + b\right)}\right)}}{2} 
i*(((im(a) + im(c))*(re(a) + re(c)) + im(a)*re(a))*re(1/(a*(a + b))) + ((re(a) + re(c))^2 + re(a)^2 - (im(a) + im(c))^2 - im(a)^2)*im(1/(a*(a + b)))/2) + ((re(a) + re(c))^2 + re(a)^2 - (im(a) + im(c))^2 - im(a)^2)*re(1/(a*(a + b)))/2 - ((im(a) + im(c))*(re(a) + re(c)) + im(a)*re(a))*im(1/(a*(a + b)))
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