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-
¿Cómo usar?
- Desigualdades:
-
(x+4)*(x-2)<0
-
x^2-17x+72<0
- (4-x)/(x-5)>=1/(1-x)
-
x-5/4-x+1/3>2
-
Expresiones idénticas
- x+ uno /(tres -x)³(x- uno) dos > cero
- x más 1 dividir por (3 menos x)³(x menos 1)2 más 0
- x más uno dividir por (tres menos x)³(x menos uno) dos más cero
- x+1/3-x³x-12>0
- x+1 dividir por (3-x)³(x-1)2>0
-
Expresiones semejantes
- x+1/(3+x)³(x-1)2>0
- x+1/(3-x)³(x+1)2>0
- x-1/(3-x)³(x-1)2>0
x+1/(3-x)³(x-1)2>0 desigualdades
Solución
Ha introducido
[src]
x - 1
x + --------*2 > 0
3
(3 - x)
$$x + 2 \frac{x - 1}{\left(3 - x\right)^{3}} > 0$$
x + 2*((x - 1)/(3 - x)^3) > 0
Solución detallada
Se da la desigualdad:
$$x + 2 \frac{x - 1}{\left(3 - x\right)^{3}} > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$x + 2 \frac{x - 1}{\left(3 - x\right)^{3}} = 0$$
Resolvemos:
$$x_{1} = - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} + \frac{9}{4}$$
$$x_{2} = \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4} - \frac{\sqrt{- \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}} - 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2}}}{2}$$
$$x_{3} = \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4} + \frac{\sqrt{- \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}} - 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2}}}{2}$$
$$x_{4} = - \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4}$$
Descartamos las soluciones complejas:
$$x_{1} = - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} + \frac{9}{4}$$
$$x_{2} = - \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4}$$
Las raíces dadas
$$x_{2} = - \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4}$$
$$x_{1} = - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} + \frac{9}{4}$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{2}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \left(- \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4}\right)$$
=
$$- \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{43}{20}$$
lo sustituimos en la expresión
$$x + 2 \frac{x - 1}{\left(3 - x\right)^{3}} > 0$$
$$2 \frac{-1 + \left(- \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{43}{20}\right)}{\left(3 - \left(- \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{43}{20}\right)\right)^{3}} + \left(- \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{43}{20}\right) > 0$$
Entonces
$$x < - \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4}$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > - \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4} \wedge x < - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} + \frac{9}{4}$$
$$x + 2 \frac{x - 1}{\left(3 - x\right)^{3}} > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$x + 2 \frac{x - 1}{\left(3 - x\right)^{3}} = 0$$
Resolvemos:
$$x_{1} = - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} + \frac{9}{4}$$
$$x_{2} = \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4} - \frac{\sqrt{- \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}} - 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2}}}{2}$$
$$x_{3} = \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4} + \frac{\sqrt{- \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}} - 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2}}}{2}$$
$$x_{4} = - \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4}$$
Descartamos las soluciones complejas:
$$x_{1} = - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} + \frac{9}{4}$$
$$x_{2} = - \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4}$$
Las raíces dadas
$$x_{2} = - \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4}$$
$$x_{1} = - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} + \frac{9}{4}$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{2}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \left(- \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4}\right)$$
=
$$- \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{43}{20}$$
lo sustituimos en la expresión
$$x + 2 \frac{x - 1}{\left(3 - x\right)^{3}} > 0$$
$$2 \frac{-1 + \left(- \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{43}{20}\right)}{\left(3 - \left(- \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{43}{20}\right)\right)^{3}} + \left(- \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{43}{20}\right) > 0$$
/ _________________________________________________________________________________________________________________________\
| / _______________ |
_________________________________________________________________________________________________________________________ | / / ______ |
/ _______________ | / 9 / \/ 5934 5 11 |
/ / ______ | / - - 2*3 / -2 + -------- + ---------------------- + ----------------------------------------------------------------- |
/ 9 / \/ 5934 5 11 | _____________________________________________________ / 2 \/ 36 _______________ _____________________________________________________ |
/ - - 2*3 / -2 + -------- + ---------------------- + ----------------------------------------------------------------- | / _______________ / / ______ / _______________ |
_____________________________________________________ / 2 \/ 36 _______________ _____________________________________________________ | / / ______ / / \/ 5934 / / ______ |
/ _______________ / / ______ / _______________ | / 9 / \/ 5934 5 / 3*3 / -2 + -------- / 9 / \/ 5934 5 |
/ / ______ / / \/ 5934 / / ______ | / - + 2*3 / -2 + -------- - ---------------------- / \/ 36 4* / - + 2*3 / -2 + -------- - ---------------------- |
/ 9 / \/ 5934 5 / 3*3 / -2 + -------- / 9 / \/ 5934 5 | / 4 \/ 36 _______________ / / 4 \/ 36 _______________ |
/ - + 2*3 / -2 + -------- - ---------------------- / \/ 36 4* / - + 2*3 / -2 + -------- - ---------------------- | / / ______ / / / ______ |
/ 4 \/ 36 _______________ / / 4 \/ 36 _______________ | / / \/ 5934 / / / \/ 5934 |
/ / ______ / / / ______ | / 3*3 / -2 + -------- / / 3*3 / -2 + -------- |
/ / \/ 5934 / / / \/ 5934 |23 \/ \/ 36 \/ \/ \/ 36 |
/ 3*3 / -2 + -------- / / 3*3 / -2 + -------- 2*|-- - --------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------|
43 \/ \/ 36 \/ \/ \/ 36 \20 2 2 /
-- - --------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
20 2 2 3 > 0
/ _________________________________________________________________________________________________________________________\
| / _______________ |
| / / ______ |
| / 9 / \/ 5934 5 11 |
| / - - 2*3 / -2 + -------- + ---------------------- + ----------------------------------------------------------------- |
| _____________________________________________________ / 2 \/ 36 _______________ _____________________________________________________ |
| / _______________ / / ______ / _______________ |
| / / ______ / / \/ 5934 / / ______ |
| / 9 / \/ 5934 5 / 3*3 / -2 + -------- / 9 / \/ 5934 5 |
| / - + 2*3 / -2 + -------- - ---------------------- / \/ 36 4* / - + 2*3 / -2 + -------- - ---------------------- |
| / 4 \/ 36 _______________ / / 4 \/ 36 _______________ |
| / / ______ / / / ______ |
| / / \/ 5934 / / / \/ 5934 |
| / 3*3 / -2 + -------- / / 3*3 / -2 + -------- |
|17 \/ \/ 36 \/ \/ \/ 36 |
|-- + --------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------|
\20 2 2 /
Entonces
$$x < - \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4}$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > - \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{9}{4} \wedge x < - \frac{\sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + \frac{9}{2} + \frac{11}{4 \sqrt{- \frac{5}{3 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}}} + 2 \sqrt[3]{-2 + \frac{\sqrt{5934}}{36}} + \frac{9}{4}}}}}{2} + \frac{9}{4}$$
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x2 x1
Solución de la desigualdad en el gráfico
Respuesta rápida
[src]
/ / / 4 3 2 \ \ / / 4 3 2 \ \\ Or\And\x < 3, CRootOf\x - 9*x + 27*x - 29*x + 2, 0/ < x/, And\x < oo, CRootOf\x - 9*x + 27*x - 29*x + 2, 1/ < x//
$$\left(x < 3 \wedge \operatorname{CRootOf} {\left(x^{4} - 9 x^{3} + 27 x^{2} - 29 x + 2, 0\right)} < x\right) \vee \left(x < \infty \wedge \operatorname{CRootOf} {\left(x^{4} - 9 x^{3} + 27 x^{2} - 29 x + 2, 1\right)} < x\right)$$
((x < 3)∧(CRootOf(x^4 - 9*x^3 + 27*x^2 - 29*x + 2, 0) < x))∨((x < oo)∧(CRootOf(x^4 - 9*x^3 + 27*x^2 - 29*x + 2, 1) < x))
Respuesta rápida 2
[src]
/ 4 3 2 \ / 4 3 2 \ (CRootOf\x - 9*x + 27*x - 29*x + 2, 0/, 3) U (CRootOf\x - 9*x + 27*x - 29*x + 2, 1/, oo)
$$x\ in\ \left(\operatorname{CRootOf} {\left(x^{4} - 9 x^{3} + 27 x^{2} - 29 x + 2, 0\right)}, 3\right) \cup \left(\operatorname{CRootOf} {\left(x^{4} - 9 x^{3} + 27 x^{2} - 29 x + 2, 1\right)}, \infty\right)$$
x in Union(Interval.open(CRootOf(x^4 - 9*x^3 + 27*x^2 - 29*x + 2, 0), 3), Interval.open(CRootOf(x^4 - 9*x^3 + 27*x^2 - 29*x + 2, 1), oo))