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sqrt(9a^2-b^2) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   ___________    
  /    2    2     
\/  9*a  - b   = 0
9a2−b2=0\sqrt{9 a^{2} - b^{2}} = 0
Simplificar
Solución detallada
9a2−b2=0\sqrt{9 a^{2} - b^{2}} = 0
cambiamos
9a2−b2=09 a^{2} - b^{2} = 0
Es la ecuación de la forma
a*b^2 + b*b + c = 0

La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
b1=D−b2ab_{1} = \frac{\sqrt{D} - b}{2 a}
b2=−D−b2ab_{2} = \frac{- \sqrt{D} - b}{2 a}
donde D = b^2 - 4*a*c es el discriminante.
Como
a=−1a = -1
b=0b = 0
c=9a2c = 9 a^{2}
, entonces
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (-1) * (9*a^2) = 36*a^2

La ecuación tiene dos raíces.
b1 = (-b + sqrt(D)) / (2*a)

b2 = (-b - sqrt(D)) / (2*a)

o
b1=−3a2b_{1} = - 3 \sqrt{a^{2}}
b2=3a2b_{2} = 3 \sqrt{a^{2}}
Gráfica
Respuesta rápida [src] 
             ______________________________________                                                      ______________________________________                                           
            /                  2                       /     /                 2        2   \\          /                  2                       /     /                 2        2   \\
         4 /  /  2        2   \        2      2        |atan2\2*im(a)*re(a), re (a) - im (a)/|       4 /  /  2        2   \        2      2        |atan2\2*im(a)*re(a), re (a) - im (a)/|
b1 = - 3*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *cos|-------------------------------------| - 3*I*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *sin|-------------------------------------|
                                                       \                  2                  /                                                     \                  2                  /
b1=−3i((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))24sin⁡(atan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)2)−3((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))24cos⁡(atan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)2)b_{1} = - 3 i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - 3 \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} 
           ______________________________________                                                      ______________________________________                                           
          /                  2                       /     /                 2        2   \\          /                  2                       /     /                 2        2   \\
       4 /  /  2        2   \        2      2        |atan2\2*im(a)*re(a), re (a) - im (a)/|       4 /  /  2        2   \        2      2        |atan2\2*im(a)*re(a), re (a) - im (a)/|
b2 = 3*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *cos|-------------------------------------| + 3*I*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *sin|-------------------------------------|
                                                     \                  2                  /                                                     \                  2                  /
b2=3i((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))24sin⁡(atan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)2)+3((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))24cos⁡(atan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)2)b_{2} = 3 i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 3 \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} 
b2 = 3*i*((re(a)^2 - im(a)^2)^2 + 4*re(a)^2*im(a)^2)^(1/4)*sin(atan2(2*re(a)*im(a, re(a)^2 - im(a)^2)/2) + 3*((re(a)^2 - im(a)^2)^2 + 4*re(a)^2*im(a)^2)^(1/4)*cos(atan2(2*re(a)*im(a), re(a)^2 - im(a)^2)/2))
Suma y producto de raíces [src] 
suma
        ______________________________________                                                      ______________________________________                                                    ______________________________________                                                      ______________________________________                                           
       /                  2                       /     /                 2        2   \\          /                  2                       /     /                 2        2   \\        /                  2                       /     /                 2        2   \\          /                  2                       /     /                 2        2   \\
    4 /  /  2        2   \        2      2        |atan2\2*im(a)*re(a), re (a) - im (a)/|       4 /  /  2        2   \        2      2        |atan2\2*im(a)*re(a), re (a) - im (a)/|     4 /  /  2        2   \        2      2        |atan2\2*im(a)*re(a), re (a) - im (a)/|       4 /  /  2        2   \        2      2        |atan2\2*im(a)*re(a), re (a) - im (a)/|
- 3*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *cos|-------------------------------------| - 3*I*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *sin|-------------------------------------| + 3*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *cos|-------------------------------------| + 3*I*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *sin|-------------------------------------|
                                                  \                  2                  /                                                     \                  2                  /                                                   \                  2                  /                                                     \                  2                  /
(−3i((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))24sin⁡(atan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)2)−3((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))24cos⁡(atan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)2))+(3i((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))24sin⁡(atan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)2)+3((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))24cos⁡(atan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)2))\left(- 3 i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - 3 \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right) + \left(3 i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 3 \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right) 
=
0
00 
producto
/        ______________________________________                                                      ______________________________________                                           \ /      ______________________________________                                                      ______________________________________                                           \
|       /                  2                       /     /                 2        2   \\          /                  2                       /     /                 2        2   \\| |     /                  2                       /     /                 2        2   \\          /                  2                       /     /                 2        2   \\|
|    4 /  /  2        2   \        2      2        |atan2\2*im(a)*re(a), re (a) - im (a)/|       4 /  /  2        2   \        2      2        |atan2\2*im(a)*re(a), re (a) - im (a)/|| |  4 /  /  2        2   \        2      2        |atan2\2*im(a)*re(a), re (a) - im (a)/|       4 /  /  2        2   \        2      2        |atan2\2*im(a)*re(a), re (a) - im (a)/||
|- 3*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *cos|-------------------------------------| - 3*I*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *sin|-------------------------------------||*|3*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *cos|-------------------------------------| + 3*I*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *sin|-------------------------------------||
\                                                  \                  2                  /                                                     \                  2                  // \                                                \                  2                  /                                                     \                  2                  //
(−3i((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))24sin⁡(atan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)2)−3((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))24cos⁡(atan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)2))(3i((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))24sin⁡(atan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)2)+3((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))24cos⁡(atan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)2))\left(- 3 i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - 3 \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right) \left(3 i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 3 \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right) 
=
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      /                  2                            /                 2        2   \
     /  /  2        2   \        2      2      I*atan2\2*im(a)*re(a), re (a) - im (a)/
-9*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *e
−9((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))2eiatan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)- 9 \sqrt{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}} 
-9*sqrt((re(a)^2 - im(a)^2)^2 + 4*im(a)^2*re(a)^2)*exp(i*atan2(2*im(a)*re(a), re(a)^2 - im(a)^2))
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