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absolute(x^2+3absolutex-4)=a la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
| 2            |    
|x  + 3*|x| - 4| = a
∣(x2+3∣x∣)−4∣=a\left|{\left(x^{2} + 3 \left|{x}\right|\right) - 4}\right| = a
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Respuesta rápida [src] 
False
False 
         //      __________                       \     //      __________                       \
         ||3   \/ 25 - 4*a                        |     ||3   \/ 25 - 4*a                        |
         ||- - ------------  for And(a > 0, a < 4)|     ||- - ------------  for And(a > 0, a < 4)|
x2 = I*im|<2        2                             | + re|<2        2                             |
         ||                                       |     ||                                       |
         ||      nan               otherwise      |     ||      nan               otherwise      |
         \\                                       /     \\                                       /
x2=re⁡({32−25−4a2for a>0∧a<4NaNotherwise)+iim⁡({32−25−4a2for a>0∧a<4NaNotherwise)x_{2} = \operatorname{re}{\left(\begin{cases} \frac{3}{2} - \frac{\sqrt{25 - 4 a}}{2} & \text{for}\: a > 0 \wedge a < 4 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{3}{2} - \frac{\sqrt{25 - 4 a}}{2} & \text{for}\: a > 0 \wedge a < 4 \\\text{NaN} & \text{otherwise} \end{cases}\right)} 
         //      __________            \     //      __________            \
         ||3   \/ 25 + 4*a             |     ||3   \/ 25 + 4*a             |
         ||- - ------------  for a >= 0|     ||- - ------------  for a >= 0|
x3 = I*im|<2        2                  | + re|<2        2                  |
         ||                            |     ||                            |
         ||      nan         otherwise |     ||      nan         otherwise |
         \\                            /     \\                            /
x3=re⁡({32−4a+252for a≥0NaNotherwise)+iim⁡({32−4a+252for a≥0NaNotherwise)x_{3} = \operatorname{re}{\left(\begin{cases} \frac{3}{2} - \frac{\sqrt{4 a + 25}}{2} & \text{for}\: a \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{3}{2} - \frac{\sqrt{4 a + 25}}{2} & \text{for}\: a \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} 
         //        __________                        \     //        __________                        \
         ||  3   \/ 25 - 4*a                         |     ||  3   \/ 25 - 4*a                         |
         ||- - + ------------  for And(a <= 4, a > 0)|     ||- - + ------------  for And(a <= 4, a > 0)|
x4 = I*im|<  2        2                              | + re|<  2        2                              |
         ||                                          |     ||                                          |
         ||       nan                otherwise       |     ||       nan                otherwise       |
         \\                                          /     \\                                          /
x4=re⁡({25−4a2−32for a≤4∧a>0NaNotherwise)+iim⁡({25−4a2−32for a≤4∧a>0NaNotherwise)x_{4} = \operatorname{re}{\left(\begin{cases} \frac{\sqrt{25 - 4 a}}{2} - \frac{3}{2} & \text{for}\: a \leq 4 \wedge a > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{\sqrt{25 - 4 a}}{2} - \frac{3}{2} & \text{for}\: a \leq 4 \wedge a > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} 
         //        __________            __________      \     //        __________            __________      \
         ||  3   \/ 25 + 4*a       3   \/ 25 + 4*a       |     ||  3   \/ 25 + 4*a       3   \/ 25 + 4*a       |
         ||- - - ------------  for - + ------------ <= -1|     ||- - - ------------  for - + ------------ <= -1|
x5 = I*im|<  2        2            2        2            | + re|<  2        2            2        2            |
         ||                                              |     ||                                              |
         ||       nan                  otherwise         |     ||       nan                  otherwise         |
         \\                                              /     \\                                              /
x5=re⁡({−4a+252−32for 4a+252+32≤−1NaNotherwise)+iim⁡({−4a+252−32for 4a+252+32≤−1NaNotherwise)x_{5} = \operatorname{re}{\left(\begin{cases} - \frac{\sqrt{4 a + 25}}{2} - \frac{3}{2} & \text{for}\: \frac{\sqrt{4 a + 25}}{2} + \frac{3}{2} \leq -1 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{\sqrt{4 a + 25}}{2} - \frac{3}{2} & \text{for}\: \frac{\sqrt{4 a + 25}}{2} + \frac{3}{2} \leq -1 \\\text{NaN} & \text{otherwise} \end{cases}\right)} 
         //        __________              __________     \     //        __________              __________     \
         ||  3   \/ 25 + 4*a         3   \/ 25 + 4*a      |     ||  3   \/ 25 + 4*a         3   \/ 25 + 4*a      |
         ||- - + ------------  for - - + ------------ >= 1|     ||- - + ------------  for - - + ------------ >= 1|
x6 = I*im|<  2        2              2        2           | + re|<  2        2              2        2           |
         ||                                               |     ||                                               |
         ||       nan                   otherwise         |     ||       nan                   otherwise         |
         \\                                               /     \\                                               /
x6=re⁡({4a+252−32for 4a+252−32≥1NaNotherwise)+iim⁡({4a+252−32for 4a+252−32≥1NaNotherwise)x_{6} = \operatorname{re}{\left(\begin{cases} \frac{\sqrt{4 a + 25}}{2} - \frac{3}{2} & \text{for}\: \frac{\sqrt{4 a + 25}}{2} - \frac{3}{2} \geq 1 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{\sqrt{4 a + 25}}{2} - \frac{3}{2} & \text{for}\: \frac{\sqrt{4 a + 25}}{2} - \frac{3}{2} \geq 1 \\\text{NaN} & \text{otherwise} \end{cases}\right)} 
x6 = re(Piecewise((sqrt(4*a + 25/2 - 3/2, sqrt(4*a + 25)/2 - 3/2 >= 1), (nan, True))) + i*im(Piecewise((sqrt(4*a + 25)/2 - 3/2, sqrt(4*a + 25)/2 - 3/2 >= 1), (nan, True))))
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