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2*(-2*x*(2*x-5)/(x^2+1)+1+(4*x^2/(x^2+1)-1)*(x^2-5*x+3)/(x^2+1))/(x^2+1)=0 la ecuación

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v

Solución numérica:

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Solución

Ha introducido [src]
  /                     /    2     \               \    
  |                     | 4*x      | / 2          \|    
  |                     |------ - 1|*\x  - 5*x + 3/|    
  |                     | 2        |               |    
  |-2*x*(2*x - 5)       \x  + 1    /               |    
2*|-------------- + 1 + ---------------------------|    
  |     2                           2              |    
  \    x  + 1                      x  + 1          /    
---------------------------------------------------- = 0
                        2                               
                       x  + 1                           
$$\frac{2 \left(\frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \left(\left(x^{2} - 5 x\right) + 3\right)}{x^{2} + 1} + \left(\frac{- 2 x \left(2 x - 5\right)}{x^{2} + 1} + 1\right)\right)}{x^{2} + 1} = 0$$
Gráfica
Respuesta rápida [src]
              /               1                \     /     /               1                \                                                \                                                
         29*re|--------------------------------|     |29*im|--------------------------------|                                                |                                                
              |/          ___\     ____________|     |     |/          ___\     ____________|                                                |                                                
              ||  1   I*\/ 3 |    /  58   29*I |     |     ||  1   I*\/ 3 |    /  58   29*I |     ____    /atan(5/2)\     ____    /atan(5/2)\|     ____    /atan(5/2)\     ____    /atan(5/2)\
              ||- - - -------|*3 /  --- + ---- |     |     ||- - - -------|*3 /  --- + ---- |   \/ 29 *sin|---------|   \/ 87 *cos|---------||   \/ 29 *cos|---------|   \/ 87 *sin|---------|
     2        \\  2      2   / \/   125    25  /     |     \\  2      2   / \/   125    25  /             \    3    /             \    3    /|             \    3    /             \    3    /
x1 = - + --------------------------------------- + I*|--------------------------------------- - --------------------- - ---------------------| - --------------------- + ---------------------
     5                      25                       \                   25                               10                      10         /             10                      10         
$$x_{1} = - \frac{\sqrt{29} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{29 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25} + \frac{\sqrt{87} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{2}{5} + i \left(- \frac{\sqrt{87} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} - \frac{\sqrt{29} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{29 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25}\right)$$
              /               1                \     /     /               1                \                                                \                                                
         29*re|--------------------------------|     |29*im|--------------------------------|                                                |                                                
              |/          ___\     ____________|     |     |/          ___\     ____________|                                                |                                                
              ||  1   I*\/ 3 |    /  58   29*I |     |     ||  1   I*\/ 3 |    /  58   29*I |     ____    /atan(5/2)\     ____    /atan(5/2)\|     ____    /atan(5/2)\     ____    /atan(5/2)\
              ||- - + -------|*3 /  --- + ---- |     |     ||- - + -------|*3 /  --- + ---- |   \/ 29 *sin|---------|   \/ 87 *cos|---------||   \/ 29 *cos|---------|   \/ 87 *sin|---------|
     2        \\  2      2   / \/   125    25  /     |     \\  2      2   / \/   125    25  /             \    3    /             \    3    /|             \    3    /             \    3    /
x2 = - + --------------------------------------- + I*|--------------------------------------- - --------------------- + ---------------------| - --------------------- - ---------------------
     5                      25                       \                   25                               10                      10         /             10                      10         
$$x_{2} = \frac{29 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25} - \frac{\sqrt{29} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} - \frac{\sqrt{87} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{2}{5} + i \left(\frac{29 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25} - \frac{\sqrt{29} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{\sqrt{87} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10}\right)$$
             ____________                      
     2      /  58   29*I             29        
x3 = - + 3 /  --- + ----  + -------------------
     5   \/   125    25            ____________
                                  /  58   29*I 
                            25*3 /  --- + ---- 
                               \/   125    25  
$$x_{3} = \frac{2}{5} + \frac{29}{25 \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}} + \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}$$
x3 = 2/5 + 29/(25*(58/125 + 29*i/25)^(1/3)) + (58/125 + 29*i/25)^(1/3)
Suma y producto de raíces [src]
suma
         /               1                \     /     /               1                \                                                \                                                            /               1                \     /     /               1                \                                                \                                                                                             
    29*re|--------------------------------|     |29*im|--------------------------------|                                                |                                                       29*re|--------------------------------|     |29*im|--------------------------------|                                                |                                                                                             
         |/          ___\     ____________|     |     |/          ___\     ____________|                                                |                                                            |/          ___\     ____________|     |     |/          ___\     ____________|                                                |                                                                                             
         ||  1   I*\/ 3 |    /  58   29*I |     |     ||  1   I*\/ 3 |    /  58   29*I |     ____    /atan(5/2)\     ____    /atan(5/2)\|     ____    /atan(5/2)\     ____    /atan(5/2)\            ||  1   I*\/ 3 |    /  58   29*I |     |     ||  1   I*\/ 3 |    /  58   29*I |     ____    /atan(5/2)\     ____    /atan(5/2)\|     ____    /atan(5/2)\     ____    /atan(5/2)\                                             
         ||- - - -------|*3 /  --- + ---- |     |     ||- - - -------|*3 /  --- + ---- |   \/ 29 *sin|---------|   \/ 87 *cos|---------||   \/ 29 *cos|---------|   \/ 87 *sin|---------|            ||- - + -------|*3 /  --- + ---- |     |     ||- - + -------|*3 /  --- + ---- |   \/ 29 *sin|---------|   \/ 87 *cos|---------||   \/ 29 *cos|---------|   \/ 87 *sin|---------|           ____________                      
2        \\  2      2   / \/   125    25  /     |     \\  2      2   / \/   125    25  /             \    3    /             \    3    /|             \    3    /             \    3    /   2        \\  2      2   / \/   125    25  /     |     \\  2      2   / \/   125    25  /             \    3    /             \    3    /|             \    3    /             \    3    /   2      /  58   29*I             29        
- + --------------------------------------- + I*|--------------------------------------- - --------------------- - ---------------------| - --------------------- + --------------------- + - + --------------------------------------- + I*|--------------------------------------- - --------------------- + ---------------------| - --------------------- - --------------------- + - + 3 /  --- + ----  + -------------------
5                      25                       \                   25                               10                      10         /             10                      10            5                      25                       \                   25                               10                      10         /             10                      10            5   \/   125    25            ____________
                                                                                                                                                                                                                                                                                                                                                                                                                     /  58   29*I 
                                                                                                                                                                                                                                                                                                                                                                                                               25*3 /  --- + ---- 
                                                                                                                                                                                                                                                                                                                                                                                                                  \/   125    25  
$$\left(\frac{2}{5} + \frac{29}{25 \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}} + \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}\right) + \left(\left(- \frac{\sqrt{29} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{29 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25} + \frac{\sqrt{87} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{2}{5} + i \left(- \frac{\sqrt{87} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} - \frac{\sqrt{29} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{29 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25}\right)\right) + \left(\frac{29 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25} - \frac{\sqrt{29} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} - \frac{\sqrt{87} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{2}{5} + i \left(\frac{29 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25} - \frac{\sqrt{29} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{\sqrt{87} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10}\right)\right)\right)$$
=
                                                  /               1                \        /               1                \     /     /               1                \                                                \     /     /               1                \                                                \                        
                                             29*re|--------------------------------|   29*re|--------------------------------|     |29*im|--------------------------------|                                                |     |29*im|--------------------------------|                                                |                        
                                                  |/          ___\     ____________|        |/          ___\     ____________|     |     |/          ___\     ____________|                                                |     |     |/          ___\     ____________|                                                |                        
                                                  ||  1   I*\/ 3 |    /  58   29*I |        ||  1   I*\/ 3 |    /  58   29*I |     |     ||  1   I*\/ 3 |    /  58   29*I |     ____    /atan(5/2)\     ____    /atan(5/2)\|     |     ||  1   I*\/ 3 |    /  58   29*I |     ____    /atan(5/2)\     ____    /atan(5/2)\|     ____    /atan(5/2)\
        ____________                              ||- - + -------|*3 /  --- + ---- |        ||- - - -------|*3 /  --- + ---- |     |     ||- - + -------|*3 /  --- + ---- |   \/ 29 *sin|---------|   \/ 87 *cos|---------||     |     ||- - - -------|*3 /  --- + ---- |   \/ 29 *sin|---------|   \/ 87 *cos|---------||   \/ 29 *cos|---------|
6      /  58   29*I             29                \\  2      2   / \/   125    25  /        \\  2      2   / \/   125    25  /     |     \\  2      2   / \/   125    25  /             \    3    /             \    3    /|     |     \\  2      2   / \/   125    25  /             \    3    /             \    3    /|             \    3    /
- + 3 /  --- + ----  + ------------------- + --------------------------------------- + --------------------------------------- + I*|--------------------------------------- - --------------------- + ---------------------| + I*|--------------------------------------- - --------------------- - ---------------------| - ---------------------
5   \/   125    25            ____________                      25                                        25                       \                   25                               10                      10         /     \                   25                               10                      10         /             5          
                             /  58   29*I                                                                                                                                                                                                                                                                                                         
                       25*3 /  --- + ----                                                                                                                                                                                                                                                                                                         
                          \/   125    25                                                                                                                                                                                                                                                                                                          
$$- \frac{\sqrt{29} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{5} + \frac{29 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25} + \frac{29 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25} + \frac{6}{5} + \frac{29}{25 \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}} + i \left(- \frac{\sqrt{87} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} - \frac{\sqrt{29} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{29 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25}\right) + i \left(\frac{29 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25} - \frac{\sqrt{29} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{\sqrt{87} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10}\right) + \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}$$
producto
/         /               1                \     /     /               1                \                                                \                                                \ /         /               1                \     /     /               1                \                                                \                                                \                                             
|    29*re|--------------------------------|     |29*im|--------------------------------|                                                |                                                | |    29*re|--------------------------------|     |29*im|--------------------------------|                                                |                                                |                                             
|         |/          ___\     ____________|     |     |/          ___\     ____________|                                                |                                                | |         |/          ___\     ____________|     |     |/          ___\     ____________|                                                |                                                |                                             
|         ||  1   I*\/ 3 |    /  58   29*I |     |     ||  1   I*\/ 3 |    /  58   29*I |     ____    /atan(5/2)\     ____    /atan(5/2)\|     ____    /atan(5/2)\     ____    /atan(5/2)\| |         ||  1   I*\/ 3 |    /  58   29*I |     |     ||  1   I*\/ 3 |    /  58   29*I |     ____    /atan(5/2)\     ____    /atan(5/2)\|     ____    /atan(5/2)\     ____    /atan(5/2)\|                                             
|         ||- - - -------|*3 /  --- + ---- |     |     ||- - - -------|*3 /  --- + ---- |   \/ 29 *sin|---------|   \/ 87 *cos|---------||   \/ 29 *cos|---------|   \/ 87 *sin|---------|| |         ||- - + -------|*3 /  --- + ---- |     |     ||- - + -------|*3 /  --- + ---- |   \/ 29 *sin|---------|   \/ 87 *cos|---------||   \/ 29 *cos|---------|   \/ 87 *sin|---------|| /        ____________                      \
|2        \\  2      2   / \/   125    25  /     |     \\  2      2   / \/   125    25  /             \    3    /             \    3    /|             \    3    /             \    3    /| |2        \\  2      2   / \/   125    25  /     |     \\  2      2   / \/   125    25  /             \    3    /             \    3    /|             \    3    /             \    3    /| |2      /  58   29*I             29        |
|- + --------------------------------------- + I*|--------------------------------------- - --------------------- - ---------------------| - --------------------- + ---------------------|*|- + --------------------------------------- + I*|--------------------------------------- - --------------------- + ---------------------| - --------------------- - ---------------------|*|- + 3 /  --- + ----  + -------------------|
\5                      25                       \                   25                               10                      10         /             10                      10         / \5                      25                       \                   25                               10                      10         /             10                      10         / |5   \/   125    25            ____________|
                                                                                                                                                                                                                                                                                                                                                                                        |                             /  58   29*I |
                                                                                                                                                                                                                                                                                                                                                                                        |                       25*3 /  --- + ---- |
                                                                                                                                                                                                                                                                                                                                                                                        \                          \/   125    25  /
$$\left(- \frac{\sqrt{29} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{29 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25} + \frac{\sqrt{87} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{2}{5} + i \left(- \frac{\sqrt{87} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} - \frac{\sqrt{29} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{29 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25}\right)\right) \left(\frac{29 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25} - \frac{\sqrt{29} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} - \frac{\sqrt{87} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{2}{5} + i \left(\frac{29 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}}\right)}}{25} - \frac{\sqrt{29} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10} + \frac{\sqrt{87} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}}{10}\right)\right) \left(\frac{2}{5} + \frac{29}{25 \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}} + \sqrt[3]{\frac{58}{125} + \frac{29 i}{25}}\right)$$
=
  2/3 /     3 ____________ /    3 ____________\\ /            /2*atan(5/2)\       ____    /atan(5/2)\\
29   *\29 + \/ 58 + 145*I *\2 + \/ 58 + 145*I //*|-25 + 58*cos|-----------| - 4*\/ 29 *cos|---------||
                                                 \            \     3     /               \    3    //
------------------------------------------------------------------------------------------------------
                                                3 _________                                           
                                           3625*\/ 2 + 5*I                                            
$$\frac{29^{\frac{2}{3}} \left(29 + \left(2 + \sqrt[3]{58 + 145 i}\right) \sqrt[3]{58 + 145 i}\right) \left(-25 - 4 \sqrt{29} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)} + 58 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{5}{2} \right)}}{3} \right)}\right)}{3625 \sqrt[3]{2 + 5 i}}$$
29^(2/3)*(29 + (58 + 145*i)^(1/3)*(2 + (58 + 145*i)^(1/3)))*(-25 + 58*cos(2*atan(5/2)/3) - 4*sqrt(29)*cos(atan(5/2)/3))/(3625*(2 + 5*i)^(1/3))
Respuesta numérica [src]
x1 = 23141.2871414737
x2 = 28222.9902792486
x3 = -32836.0908611716
x4 = -22671.0784609129
x5 = 37542.2581534465
x6 = 29070.0775360195
x7 = -34530.6110215311
x8 = -27753.0246082813
x9 = 27375.9358778704
x10 = -39614.5197917689
x11 = -33683.3424285563
x12 = -24364.8937154052
x13 = -26905.9389919123
x14 = 22294.5163449108
x15 = -35377.8954358315
x16 = 38389.5717165956
x17 = -40461.87927088
x18 = -36225.1945781885
x19 = -28600.1403609643
x20 = 25681.9390289484
x21 = -25211.870065014
x22 = 21447.8137095784
x23 = 30764.3394950442
x24 = 0.127520008265528
x25 = 39236.8980608255
x26 = 35000.403624952
x27 = 40084.2363610529
x28 = 26528.917568814
x29 = 20601.1879629253
x30 = -21824.2499741543
x31 = 41778.9458696908
x32 = -31141.6442642844
x33 = -30294.4523404771
x34 = -31988.857649096
x35 = 35847.6730687601
x36 = 23988.1186454862
x37 = -37919.8331556035
x38 = -42156.6273460194
x39 = 29917.1947872752
x40 = 31611.5093999564
x41 = -38767.1708545838
x42 = -29447.2836960679
x43 = -20977.4825624709
x44 = 40931.5858617346
x45 = 36694.958274193
x46 = 33305.9169392146
x47 = 34153.1511408611
x48 = -26058.8863912926
x49 = 24835.0044525093
x50 = 2.38673073904276
x51 = -23517.9615667876
x52 = 32458.7024840204
x53 = -37072.5074538246
x54 = -20130.7837421488
x55 = 42626.3157477988
x56 = -41309.2486520078
x56 = -41309.2486520078