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ln(|x|)/2=-ln(|p-1|)+C la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
log(|x|)                    
-------- = -log(|p - 1|) + c
   2
log⁡(∣x∣)2=c−log⁡(∣p−1∣)\frac{\log{\left(\left|{x}\right| \right)}}{2} = c - \log{\left(\left|{p - 1}\right| \right)}
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
    //    2*c             2*c        \     //    2*c             2*c        \       //     2*c              2*c       \     //     2*c              2*c       \
    ||   e               e           |     ||   e               e           |       ||   -e                e          |     ||   -e                e          |
    ||---------  for ----------- >= 0|     ||---------  for ----------- >= 0|       ||-----------  for ----------- > 0|     ||-----------  for ----------- > 0|
I*im|<        2      |        2|     | + re|<        2      |        2|     | + I*im|<|        2|      |        2|    | + re|<|        2|      |        2|    |
    |||-1 + p|       |(-1 + p) |     |     |||-1 + p|       |(-1 + p) |     |       |||(-1 + p) |      |(-1 + p) |    |     |||(-1 + p) |      |(-1 + p) |    |
    ||                               |     ||                               |       ||                                |     ||                                |
    \\   nan          otherwise      /     \\   nan          otherwise      /       \\    nan           otherwise     /     \\    nan           otherwise     /
(re⁡({e2c∣p−1∣2for e2c∣(p−1)2∣≥0NaNotherwise)+iim⁡({e2c∣p−1∣2for e2c∣(p−1)2∣≥0NaNotherwise))+(re⁡({−e2c∣(p−1)2∣for e2c∣(p−1)2∣>0NaNotherwise)+iim⁡({−e2c∣(p−1)2∣for e2c∣(p−1)2∣>0NaNotherwise))\left(\operatorname{re}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) + \left(\operatorname{re}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) 
=
    //    2*c             2*c        \       //     2*c              2*c       \     //    2*c             2*c        \     //     2*c              2*c       \
    ||   e               e           |       ||   -e                e          |     ||   e               e           |     ||   -e                e          |
    ||---------  for ----------- >= 0|       ||-----------  for ----------- > 0|     ||---------  for ----------- >= 0|     ||-----------  for ----------- > 0|
I*im|<        2      |        2|     | + I*im|<|        2|      |        2|    | + re|<        2      |        2|     | + re|<|        2|      |        2|    |
    |||-1 + p|       |(-1 + p) |     |       |||(-1 + p) |      |(-1 + p) |    |     |||-1 + p|       |(-1 + p) |     |     |||(-1 + p) |      |(-1 + p) |    |
    ||                               |       ||                                |     ||                               |     ||                                |
    \\   nan          otherwise      /       \\    nan           otherwise     /     \\   nan          otherwise      /     \\    nan           otherwise     /
re⁡({e2c∣p−1∣2for e2c∣(p−1)2∣≥0NaNotherwise)+re⁡({−e2c∣(p−1)2∣for e2c∣(p−1)2∣>0NaNotherwise)+iim⁡({e2c∣p−1∣2for e2c∣(p−1)2∣≥0NaNotherwise)+iim⁡({−e2c∣(p−1)2∣for e2c∣(p−1)2∣>0NaNotherwise)\operatorname{re}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} 
producto
/    //    2*c             2*c        \     //    2*c             2*c        \\ /    //     2*c              2*c       \     //     2*c              2*c       \\
|    ||   e               e           |     ||   e               e           || |    ||   -e                e          |     ||   -e                e          ||
|    ||---------  for ----------- >= 0|     ||---------  for ----------- >= 0|| |    ||-----------  for ----------- > 0|     ||-----------  for ----------- > 0||
|I*im|<        2      |        2|     | + re|<        2      |        2|     ||*|I*im|<|        2|      |        2|    | + re|<|        2|      |        2|    ||
|    |||-1 + p|       |(-1 + p) |     |     |||-1 + p|       |(-1 + p) |     || |    |||(-1 + p) |      |(-1 + p) |    |     |||(-1 + p) |      |(-1 + p) |    ||
|    ||                               |     ||                               || |    ||                                |     ||                                ||
\    \\   nan          otherwise      /     \\   nan          otherwise      // \    \\    nan           otherwise     /     \\    nan           otherwise     //
(re⁡({e2c∣p−1∣2for e2c∣(p−1)2∣≥0NaNotherwise)+iim⁡({e2c∣p−1∣2for e2c∣(p−1)2∣≥0NaNotherwise))(re⁡({−e2c∣(p−1)2∣for e2c∣(p−1)2∣>0NaNotherwise)+iim⁡({−e2c∣(p−1)2∣for e2c∣(p−1)2∣>0NaNotherwise))\left(\operatorname{re}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) 
=
/  4*re(c) + 4*I*im(c)          /     2*c               2*c       \
|-e                             |    e                 e          |
|----------------------  for And|----------- >= 0, ----------- > 0|
|                2              ||        2|       |        2|    |
<     |        2|               \|(-1 + p) |       |(-1 + p) |    /
|     |(-1 + p) |                                                  
|                                                                  
|         nan                            otherwise                 
\
{−e4re⁡(c)+4iim⁡(c)∣(p−1)2∣2for e2c∣(p−1)2∣≥0∧e2c∣(p−1)2∣>0NaNotherwise\begin{cases} - \frac{e^{4 \operatorname{re}{\left(c\right)} + 4 i \operatorname{im}{\left(c\right)}}}{\left|{\left(p - 1\right)^{2}}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \wedge \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases} 
Piecewise((-exp(4*re(c) + 4*i*im(c))/Abs((-1 + p)^2)^2, (exp(2*c)/Abs((-1 + p)^2) >= 0)∧(exp(2*c)/Abs((-1 + p)^2) > 0)), (nan, True))
Respuesta rápida [src] 
         //    2*c             2*c        \     //    2*c             2*c        \
         ||   e               e           |     ||   e               e           |
         ||---------  for ----------- >= 0|     ||---------  for ----------- >= 0|
x1 = I*im|<        2      |        2|     | + re|<        2      |        2|     |
         |||-1 + p|       |(-1 + p) |     |     |||-1 + p|       |(-1 + p) |     |
         ||                               |     ||                               |
         \\   nan          otherwise      /     \\   nan          otherwise      /
x1=re⁡({e2c∣p−1∣2for e2c∣(p−1)2∣≥0NaNotherwise)+iim⁡({e2c∣p−1∣2for e2c∣(p−1)2∣≥0NaNotherwise)x_{1} = \operatorname{re}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} 
         //     2*c              2*c       \     //     2*c              2*c       \
         ||   -e                e          |     ||   -e                e          |
         ||-----------  for ----------- > 0|     ||-----------  for ----------- > 0|
x2 = I*im|<|        2|      |        2|    | + re|<|        2|      |        2|    |
         |||(-1 + p) |      |(-1 + p) |    |     |||(-1 + p) |      |(-1 + p) |    |
         ||                                |     ||                                |
         \\    nan           otherwise     /     \\    nan           otherwise     /
x2=re⁡({−e2c∣(p−1)2∣for e2c∣(p−1)2∣>0NaNotherwise)+iim⁡({−e2c∣(p−1)2∣for e2c∣(p−1)2∣>0NaNotherwise)x_{2} = \operatorname{re}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} 
x2 = re(Piecewise((-exp(2*c)/Abs((p - 1)^2, exp(2*c)/Abs((p - 1)^2) > 0), (nan, True))) + i*im(Piecewise((-exp(2*c)/Abs((p - 1)^2), exp(2*c)/Abs((p - 1)^2) > 0), (nan, True))))
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