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(x-2)*(2x-1)/2x^2+7x+3>0

(x-2)*(2x-1)/2x^2+7x+3>0 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
(x - 2)*(2*x - 1)  2              
-----------------*x  + 7*x + 3 > 0
        2                         
$$\left(x^{2} \frac{\left(x - 2\right) \left(2 x - 1\right)}{2} + 7 x\right) + 3 > 0$$
x^2*(((x - 2)*(2*x - 1))/2) + 7*x + 3 > 0
Solución detallada
Se da la desigualdad:
$$\left(x^{2} \frac{\left(x - 2\right) \left(2 x - 1\right)}{2} + 7 x\right) + 3 > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(x^{2} \frac{\left(x - 2\right) \left(2 x - 1\right)}{2} + 7 x\right) + 3 = 0$$
Resolvemos:
$$x_{1} = \frac{5}{8} + \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} - \frac{\sqrt{- \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}} - 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24}}}{2}$$
$$x_{2} = \frac{5}{8} + \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} + \frac{\sqrt{- \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}} - 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24}}}{2}$$
$$x_{3} = - \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{5}{8}$$
$$x_{4} = - \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{5}{8}$$
Descartamos las soluciones complejas:
$$x_{1} = - \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{5}{8}$$
$$x_{2} = - \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{5}{8}$$
Las raíces dadas
$$x_{1} = - \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{5}{8}$$
$$x_{2} = - \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{5}{8}$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{1}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(- \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{5}{8}\right) + - \frac{1}{10}$$
=
$$- \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{21}{40}$$
lo sustituimos en la expresión
$$\left(x^{2} \frac{\left(x - 2\right) \left(2 x - 1\right)}{2} + 7 x\right) + 3 > 0$$
$$\left(7 \left(- \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{21}{40}\right) + \frac{\left(-2 + \left(- \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{21}{40}\right)\right) \left(2 \left(- \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{21}{40}\right) - 1\right)}{2} \left(- \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{21}{40}\right)^{2}\right) + 3 > 0$$
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                                                                                                                                                                                                                                                      |                                                                                             /   43        /  7091   \/ 488841                 179                                                   403                                      |  |                                                                                               /   43        /  7091   \/ 488841                 179                                                   403                                      |                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                      |                                                                                            /    -- - 2*3 /   ---- + ----------  - --------------------------- + ---------------------------------------------------------------------------- |  |                                                                                              /    -- - 2*3 /   ---- + ----------  - --------------------------- + ---------------------------------------------------------------------------- |                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                      |               _______________________________________________________________             /     24     \/    1728      576                ___________________                _______________________________________________________________ |  |                 _______________________________________________________________             /     24     \/    1728      576                ___________________                _______________________________________________________________ |                                                                                                                                                                                                                                                     
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                                                                                                                                                                                                                                                      |             /             /          ________                                           /                                               /  7091   \/ 488841                /             /          ________                                 |  |               /             /          ________                                           /                                               /  7091   \/ 488841                /             /          ________                                 |                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                      |            /   43        /  7091   \/ 488841                 179                       /                                          36*3 /   ---- + ----------              /   43        /  7091   \/ 488841                 179              |  |              /   43        /  7091   \/ 488841                 179                       /                                          36*3 /   ---- + ----------              /   43        /  7091   \/ 488841                 179              |                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                      |           /    -- + 2*3 /   ---- + ----------  + ---------------------------          /                                              \/    1728      576        32*      /    -- + 2*3 /   ---- + ----------  + ---------------------------  |  |             /    -- + 2*3 /   ---- + ----------  + ---------------------------          /                                              \/    1728      576        32*      /    -- + 2*3 /   ---- + ----------  + ---------------------------  |                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                      |          /     48     \/    1728      576                ___________________         /                                                                                  /     48     \/    1728      576                ___________________  |  |            /     48     \/    1728      576                ___________________         /                                                                                  /     48     \/    1728      576                ___________________  |                                                                                                                                                                                                                                                     
                                                                                                     ______________________________________________________________________________________________________________________________________________   |         /                                               /          ________         /                                                                                  /                                               /          ________   |  |           /                                               /          ________         /                                                                                  /                                               /          ________   | /               _______________________________________________________________                  ______________________________________________________________________________________________________________________________________________\    
                                                                                                    /             ___________________                                                                                                                 |        /                                               /  7091   \/ 488841         /                                                                                  /                                               /  7091   \/ 488841    |  |          /                                               /  7091   \/ 488841         /                                                                                  /                                               /  7091   \/ 488841    | |              /             ___________________                                                /             ___________________                                                                                                              |    
                                                                                                   /             /          ________                                                                                                                  |       /                                          36*3 /   ---- + ----------       /                                                                                  /                                          36*3 /   ---- + ----------   |  |         /                                          36*3 /   ---- + ----------       /                                                                                  /                                          36*3 /   ---- + ----------   | |             /             /          ________                                                /             /          ________                                                                                                               | > 0
                                                                                                  /   43        /  7091   \/ 488841                 179                                                   403                                         |21   \/                                              \/    1728      576         \/                                                                                 \/                                              \/    1728      576       |  |  59   \/                                              \/    1728      576         \/                                                                                 \/                                              \/    1728      576       | |1           /   43        /  7091   \/ 488841                 179                            /   43        /  7091   \/ 488841                 179                                                   403                                      |    
                                                                                    7*           /    -- - 2*3 /   ---- + ----------  - --------------------------- + ----------------------------------------------------------------------------    |-- - ------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------| *|- -- - ------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------|*|-- -       /    -- + 2*3 /   ---- + ----------  + ---------------------------  -            /    -- - 2*3 /   ---- + ----------  - --------------------------- + ---------------------------------------------------------------------------- |    
                  _______________________________________________________________               /     24     \/    1728      576                ___________________                _______________________________________________________________    \40                                       2                                                                                                                     2                                                                              /  \  40                                       2                                                                                                                     2                                                                              / |20        /     48     \/    1728      576                ___________________              /     24     \/    1728      576                ___________________                _______________________________________________________________ |    
                 /             ___________________                                             /                                               /          ________                /             ___________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        |         /                                               /          ________              /                                               /          ________                /             ___________________                                |    
                /             /          ________                                             /                                               /  7091   \/ 488841                /             /          ________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |        /                                               /  7091   \/ 488841              /                                               /  7091   \/ 488841                /             /          ________                                 |    
               /   43        /  7091   \/ 488841                 179                         /                                          36*3 /   ---- + ----------              /   43        /  7091   \/ 488841                 179                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |       /                                          36*3 /   ---- + ----------            /                                          36*3 /   ---- + ----------              /   43        /  7091   \/ 488841                 179              |    
      7*      /    -- + 2*3 /   ---- + ----------  + ---------------------------            /                                              \/    1728      576        32*      /    -- + 2*3 /   ---- + ----------  + ---------------------------                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |     \/                                              \/    1728      576               /                                              \/    1728      576        32*      /    -- + 2*3 /   ---- + ----------  + ---------------------------  |    
             /     48     \/    1728      576                ___________________           /                                                                                  /     48     \/    1728      576                ___________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |                                                                                      /                                                                                  /     48     \/    1728      576                ___________________  |    
            /                                               /          ________           /                                                                                  /                                               /          ________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           |                                                                                     /                                                                                  /                                               /          ________   |    
           /                                               /  7091   \/ 488841           /                                                                                  /                                               /  7091   \/ 488841                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |                                                                                    /                                                                                  /                                               /  7091   \/ 488841    |    
          /                                          36*3 /   ---- + ----------         /                                                                                  /                                          36*3 /   ---- + ----------                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           |                                                                                   /                                                                                  /                                          36*3 /   ---- + ----------   |    
267     \/                                              \/    1728      576           \/                                                                                 \/                                              \/    1728      576                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \                                                                                 \/                                                                                 \/                                              \/    1728      576       /    
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 40                                        2                                                                                                                       2                                                                                                                                                                                                                                                                                                                                                                                                                                                            2                                                                                                                                                                                                                                                                                                                                                                              

significa que una de las soluciones de nuestra ecuación será con:
$$x < - \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{5}{8}$$
 _____           _____          
      \         /
-------ο-------ο-------
       x1      x2

Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < - \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{5}{8}$$
$$x > - \frac{\sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}} - \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + \frac{43}{24} + \frac{403}{32 \sqrt{\frac{43}{48} + \frac{179}{36 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}} + 2 \sqrt[3]{\frac{\sqrt{488841}}{576} + \frac{7091}{1728}}}}}}{2} + \frac{5}{8}$$
Solución de la desigualdad en el gráfico
Respuesta rápida [src]
  /   /                    /   4      3      2              \\     /               /   4      3      2              \    \\
Or\And\-oo < x, x < CRootOf\2*x  - 5*x  + 2*x  + 14*x + 6, 0//, And\x < oo, CRootOf\2*x  - 5*x  + 2*x  + 14*x + 6, 1/ < x//
$$\left(-\infty < x \wedge x < \operatorname{CRootOf} {\left(2 x^{4} - 5 x^{3} + 2 x^{2} + 14 x + 6, 0\right)}\right) \vee \left(x < \infty \wedge \operatorname{CRootOf} {\left(2 x^{4} - 5 x^{3} + 2 x^{2} + 14 x + 6, 1\right)} < x\right)$$
((-oo < x)∧(x < CRootOf(2*x^4 - 5*x^3 + 2*x^2 + 14*x + 6, 0)))∨((x < oo)∧(CRootOf(2*x^4 - 5*x^3 + 2*x^2 + 14*x + 6, 1) < x))
Respuesta rápida 2 [src]
             /   4      3      2              \            /   4      3      2              \     
(-oo, CRootOf\2*x  - 5*x  + 2*x  + 14*x + 6, 0/) U (CRootOf\2*x  - 5*x  + 2*x  + 14*x + 6, 1/, oo)
$$x\ in\ \left(-\infty, \operatorname{CRootOf} {\left(2 x^{4} - 5 x^{3} + 2 x^{2} + 14 x + 6, 0\right)}\right) \cup \left(\operatorname{CRootOf} {\left(2 x^{4} - 5 x^{3} + 2 x^{2} + 14 x + 6, 1\right)}, \infty\right)$$
x in Union(Interval.open(-oo, CRootOf(2*x^4 - 5*x^3 + 2*x^2 + 14*x + 6, 0)), Interval.open(CRootOf(2*x^4 - 5*x^3 + 2*x^2 + 14*x + 6, 1), oo))
Gráfico
(x-2)*(2x-1)/2x^2+7x+3>0 desigualdades