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1-a-(a/sqrt(1-y^2))=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
             a         
1 - a - ----------- = 0
           ________    
          /      2     
        \/  1 - y
−a1−y2+(1−a)=0- \frac{a}{\sqrt{1 - y^{2}}} + \left(1 - a\right) = 0
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
                                                    /     /   /     2   \        /     2   \\\                                                       /     /   /     2   \        /     2   \\\                                                     /     /   /     2   \        /     2   \\\                                                       /     /   /     2   \        /     2   \\\
         _______________________________________    |     |   |    a    |        |    a    |||            _______________________________________    |     |   |    a    |        |    a    |||          _______________________________________    |     |   |    a    |        |    a    |||            _______________________________________    |     |   |    a    |        |    a    |||
        /                    2                      |atan2|-im|---------|, 1 - re|---------|||           /                    2                      |atan2|-im|---------|, 1 - re|---------|||         /                    2                      |atan2|-im|---------|, 1 - re|---------|||           /                    2                      |atan2|-im|---------|, 1 - re|---------|||
       /  /      /     2   \\       /     2   \     |     |   |        2|        |        2|||          /  /      /     2   \\       /     2   \     |     |   |        2|        |        2|||        /  /      /     2   \\       /     2   \     |     |   |        2|        |        2|||          /  /      /     2   \\       /     2   \     |     |   |        2|        |        2|||
      /   |      |    a    ||      2|    a    |     |     \   \(-1 + a) /        \(-1 + a) //|         /   |      |    a    ||      2|    a    |     |     \   \(-1 + a) /        \(-1 + a) //|       /   |      |    a    ||      2|    a    |     |     \   \(-1 + a) /        \(-1 + a) //|         /   |      |    a    ||      2|    a    |     |     \   \(-1 + a) /        \(-1 + a) //|
-    /    |1 - re|---------||  + im |---------| *cos|----------------------------------------| - I*   /    |1 - re|---------||  + im |---------| *sin|----------------------------------------| +    /    |1 - re|---------||  + im |---------| *cos|----------------------------------------| + I*   /    |1 - re|---------||  + im |---------| *sin|----------------------------------------|
  4 /     |      |        2||       |        2|     \                   2                    /     4 /     |      |        2||       |        2|     \                   2                    /   4 /     |      |        2||       |        2|     \                   2                    /     4 /     |      |        2||       |        2|     \                   2                    /
  \/      \      \(-1 + a) //       \(-1 + a) /                                                    \/      \      \(-1 + a) //       \(-1 + a) /                                                  \/      \      \(-1 + a) //       \(-1 + a) /                                                    \/      \      \(-1 + a) //       \(-1 + a) /
(−i(1−re⁡(a2(a−1)2))2+(im⁡(a2(a−1)2))24sin⁡(atan2⁡(−im⁡(a2(a−1)2),1−re⁡(a2(a−1)2))2)−(1−re⁡(a2(a−1)2))2+(im⁡(a2(a−1)2))24cos⁡(atan2⁡(−im⁡(a2(a−1)2),1−re⁡(a2(a−1)2))2))+(i(1−re⁡(a2(a−1)2))2+(im⁡(a2(a−1)2))24sin⁡(atan2⁡(−im⁡(a2(a−1)2),1−re⁡(a2(a−1)2))2)+(1−re⁡(a2(a−1)2))2+(im⁡(a2(a−1)2))24cos⁡(atan2⁡(−im⁡(a2(a−1)2),1−re⁡(a2(a−1)2))2))\left(- i \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} - \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)}\right) 
=
0
00 
producto
/                                                    /     /   /     2   \        /     2   \\\                                                       /     /   /     2   \        /     2   \\\\ /                                                  /     /   /     2   \        /     2   \\\                                                       /     /   /     2   \        /     2   \\\\
|         _______________________________________    |     |   |    a    |        |    a    |||            _______________________________________    |     |   |    a    |        |    a    |||| |       _______________________________________    |     |   |    a    |        |    a    |||            _______________________________________    |     |   |    a    |        |    a    ||||
|        /                    2                      |atan2|-im|---------|, 1 - re|---------|||           /                    2                      |atan2|-im|---------|, 1 - re|---------|||| |      /                    2                      |atan2|-im|---------|, 1 - re|---------|||           /                    2                      |atan2|-im|---------|, 1 - re|---------||||
|       /  /      /     2   \\       /     2   \     |     |   |        2|        |        2|||          /  /      /     2   \\       /     2   \     |     |   |        2|        |        2|||| |     /  /      /     2   \\       /     2   \     |     |   |        2|        |        2|||          /  /      /     2   \\       /     2   \     |     |   |        2|        |        2||||
|      /   |      |    a    ||      2|    a    |     |     \   \(-1 + a) /        \(-1 + a) //|         /   |      |    a    ||      2|    a    |     |     \   \(-1 + a) /        \(-1 + a) //|| |    /   |      |    a    ||      2|    a    |     |     \   \(-1 + a) /        \(-1 + a) //|         /   |      |    a    ||      2|    a    |     |     \   \(-1 + a) /        \(-1 + a) //||
|-    /    |1 - re|---------||  + im |---------| *cos|----------------------------------------| - I*   /    |1 - re|---------||  + im |---------| *sin|----------------------------------------||*|   /    |1 - re|---------||  + im |---------| *cos|----------------------------------------| + I*   /    |1 - re|---------||  + im |---------| *sin|----------------------------------------||
|  4 /     |      |        2||       |        2|     \                   2                    /     4 /     |      |        2||       |        2|     \                   2                    /| |4 /     |      |        2||       |        2|     \                   2                    /     4 /     |      |        2||       |        2|     \                   2                    /|
\  \/      \      \(-1 + a) //       \(-1 + a) /                                                    \/      \      \(-1 + a) //       \(-1 + a) /                                               / \\/      \      \(-1 + a) //       \(-1 + a) /                                                    \/      \      \(-1 + a) //       \(-1 + a) /                                               /
(−i(1−re⁡(a2(a−1)2))2+(im⁡(a2(a−1)2))24sin⁡(atan2⁡(−im⁡(a2(a−1)2),1−re⁡(a2(a−1)2))2)−(1−re⁡(a2(a−1)2))2+(im⁡(a2(a−1)2))24cos⁡(atan2⁡(−im⁡(a2(a−1)2),1−re⁡(a2(a−1)2))2))(i(1−re⁡(a2(a−1)2))2+(im⁡(a2(a−1)2))24sin⁡(atan2⁡(−im⁡(a2(a−1)2),1−re⁡(a2(a−1)2))2)+(1−re⁡(a2(a−1)2))2+(im⁡(a2(a−1)2))24cos⁡(atan2⁡(−im⁡(a2(a−1)2),1−re⁡(a2(a−1)2))2))\left(- i \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} - \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)}\right) 
=
                                                         /   /     2   \        /     2   \\
        ________________________________________         |   |    a    |        |    a    ||
       /                     2                    I*atan2|-im|---------|, 1 - re|---------||
      /  /       /     2   \\       /     2   \          |   |        2|        |        2||
     /   |       |    a    ||      2|    a    |          \   \(-1 + a) /        \(-1 + a) //
-   /    |-1 + re|---------||  + im |---------| *e                                          
   /     |       |        2||       |        2|                                             
 \/      \       \(-1 + a) //       \(-1 + a) /
−(re⁡(a2(a−1)2)−1)2+(im⁡(a2(a−1)2))2eiatan2⁡(−im⁡(a2(a−1)2),1−re⁡(a2(a−1)2))- \sqrt{\left(\operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}} 
-sqrt((-1 + re(a^2/(-1 + a)^2))^2 + im(a^2/(-1 + a)^2)^2)*exp(i*atan2(-im(a^2/(-1 + a)^2), 1 - re(a^2/(-1 + a)^2)))
Respuesta rápida [src] 
                                                         /     /   /     2   \        /     2   \\\                                                       /     /   /     2   \        /     2   \\\
              _______________________________________    |     |   |    a    |        |    a    |||            _______________________________________    |     |   |    a    |        |    a    |||
             /                    2                      |atan2|-im|---------|, 1 - re|---------|||           /                    2                      |atan2|-im|---------|, 1 - re|---------|||
            /  /      /     2   \\       /     2   \     |     |   |        2|        |        2|||          /  /      /     2   \\       /     2   \     |     |   |        2|        |        2|||
           /   |      |    a    ||      2|    a    |     |     \   \(-1 + a) /        \(-1 + a) //|         /   |      |    a    ||      2|    a    |     |     \   \(-1 + a) /        \(-1 + a) //|
y1 = -    /    |1 - re|---------||  + im |---------| *cos|----------------------------------------| - I*   /    |1 - re|---------||  + im |---------| *sin|----------------------------------------|
       4 /     |      |        2||       |        2|     \                   2                    /     4 /     |      |        2||       |        2|     \                   2                    /
       \/      \      \(-1 + a) //       \(-1 + a) /                                                    \/      \      \(-1 + a) //       \(-1 + a) /
y1=−i(1−re⁡(a2(a−1)2))2+(im⁡(a2(a−1)2))24sin⁡(atan2⁡(−im⁡(a2(a−1)2),1−re⁡(a2(a−1)2))2)−(1−re⁡(a2(a−1)2))2+(im⁡(a2(a−1)2))24cos⁡(atan2⁡(−im⁡(a2(a−1)2),1−re⁡(a2(a−1)2))2)y_{1} = - i \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} - \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} 
                                                       /     /   /     2   \        /     2   \\\                                                       /     /   /     2   \        /     2   \\\
            _______________________________________    |     |   |    a    |        |    a    |||            _______________________________________    |     |   |    a    |        |    a    |||
           /                    2                      |atan2|-im|---------|, 1 - re|---------|||           /                    2                      |atan2|-im|---------|, 1 - re|---------|||
          /  /      /     2   \\       /     2   \     |     |   |        2|        |        2|||          /  /      /     2   \\       /     2   \     |     |   |        2|        |        2|||
         /   |      |    a    ||      2|    a    |     |     \   \(-1 + a) /        \(-1 + a) //|         /   |      |    a    ||      2|    a    |     |     \   \(-1 + a) /        \(-1 + a) //|
y2 =    /    |1 - re|---------||  + im |---------| *cos|----------------------------------------| + I*   /    |1 - re|---------||  + im |---------| *sin|----------------------------------------|
     4 /     |      |        2||       |        2|     \                   2                    /     4 /     |      |        2||       |        2|     \                   2                    /
     \/      \      \(-1 + a) //       \(-1 + a) /                                                    \/      \      \(-1 + a) //       \(-1 + a) /
y2=i(1−re⁡(a2(a−1)2))2+(im⁡(a2(a−1)2))24sin⁡(atan2⁡(−im⁡(a2(a−1)2),1−re⁡(a2(a−1)2))2)+(1−re⁡(a2(a−1)2))2+(im⁡(a2(a−1)2))24cos⁡(atan2⁡(−im⁡(a2(a−1)2),1−re⁡(a2(a−1)2))2)y_{2} = i \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} 
y2 = i*((1 - re(a^2/(a - 1)^2))^2 + im(a^2/(a - 1)^2)^2)^(1/4)*sin(atan2(-im(a^2/(a - 1)^2, 1 - re(a^2/(a - 1)^2))/2) + ((1 - re(a^2/(a - 1)^2))^2 + im(a^2/(a - 1)^2)^2)^(1/4)*cos(atan2(-im(a^2/(a - 1)^2), 1 - re(a^2/(a - 1)^2))/2))
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