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sqrt(a^2-x^2) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   _________    
  /  2    2     
\/  a  - x   = 0
a2−x2=0\sqrt{a^{2} - x^{2}} = 0
Simplificar
Solución detallada
a2−x2=0\sqrt{a^{2} - x^{2}} = 0
cambiamos
a2−x2=0a^{2} - x^{2} = 0
Es la ecuación de la forma
a*x^2 + b*x + c = 0

La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{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=a2c = a^{2}
, entonces
D = b^2 - 4 * a * c = 

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

La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

o
x1=−a2x_{1} = - \sqrt{a^{2}}
x2=a2x_{2} = \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)/|
x1 = - \/   \re (a) - im (a)/  + 4*im (a)*re (a) *cos|-------------------------------------| - I*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *sin|-------------------------------------|
                                                     \                  2                  /                                                   \                  2                  /
x1=−i((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)−((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)x_{1} = - 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)} - \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)/|
x2 = \/   \re (a) - im (a)/  + 4*im (a)*re (a) *cos|-------------------------------------| + I*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *sin|-------------------------------------|
                                                   \                  2                  /                                                   \                  2                  /
x2=i((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)+((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)x_{2} = 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)} + \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)} 
x2 = 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) + ((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)/|
- \/   \re (a) - im (a)/  + 4*im (a)*re (a) *cos|-------------------------------------| - I*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *sin|-------------------------------------| + \/   \re (a) - im (a)/  + 4*im (a)*re (a) *cos|-------------------------------------| + I*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *sin|-------------------------------------|
                                                \                  2                  /                                                   \                  2                  /                                                 \                  2                  /                                                   \                  2                  /
(−i((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)−((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))+(i((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)+((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(- 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)} - \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(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)} + \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)/||
|- \/   \re (a) - im (a)/  + 4*im (a)*re (a) *cos|-------------------------------------| - I*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *sin|-------------------------------------||*|\/   \re (a) - im (a)/  + 4*im (a)*re (a) *cos|-------------------------------------| + I*\/   \re (a) - im (a)/  + 4*im (a)*re (a) *sin|-------------------------------------||
\                                                \                  2                  /                                                   \                  2                  // \                                              \                  2                  /                                                   \                  2                  //
(−i((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)−((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))(i((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)+((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(- 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)} - \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(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)} + \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)/
-\/   \re (a) - im (a)/  + 4*im (a)*re (a) *e
−((re⁡(a))2−(im⁡(a))2)2+4(re⁡(a))2(im⁡(a))2eiatan2⁡(2re⁡(a)im⁡(a),(re⁡(a))2−(im⁡(a))2)- \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)}} 
-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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