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- Sistemas de desigualdades paso a paso
- Ecuaciones básicas paso a paso
- Sistemas de ecuaciones paso a paso
- Solución de desigualdades trigonométricas en línea
- Resolución de desigualdades exponenciales en línea
- Resolución de desigualdades con un módulo en línea
-
¿Cómo usar?
- Desigualdades:
-
-3-5x<=x+3
-
2-7x>0
-
5x^2+4x>0
-
(x+4)*(x-2)<0
-
Expresiones idénticas
- (6x/(x- dos))-√(uno dos x/(x- dos))-(12x/(x-2))^1/ cuatro > cero
- (6x dividir por (x menos 2)) menos √(12x dividir por (x menos 2)) menos (12x dividir por (x menos 2)) en el grado 1 dividir por 4 más 0
- (6x dividir por (x menos dos)) menos √(uno dos x dividir por (x menos dos)) menos (12x dividir por (x menos 2)) en el grado 1 dividir por cuatro más cero
- (6x/(x-2))-√(12x/(x-2))-(12x/(x-2))1/4>0
- 6x/x-2-√12x/x-2-12x/x-21/4>0
- 6x/x-2-√12x/x-2-12x/x-2^1/4>0
- (6x dividir por (x-2))-√(12x dividir por (x-2))-(12x dividir por (x-2))^1 dividir por 4>0
-
Expresiones semejantes
- (6x/(x-2))-√(12x/(x-2))-(12x/(x+2))^1/4>0
- (6x/(x+2))-√(12x/(x-2))-(12x/(x-2))^1/4>0
- (6x/(x-2))+√(12x/(x-2))-(12x/(x-2))^1/4>0
- (6x/(x-2))-√(12x/(x+2))-(12x/(x-2))^1/4>0
- (6x/(x-2))-√(12x/(x-2))+(12x/(x-2))^1/4>0
(6x/(x-2))-√(12x/(x-2))-(12x/(x-2))^1/4>0 desigualdades
Solución
Ha introducido
[src]
_______ _______ 6*x / 12*x / 12*x ----- - / ----- - 4 / ----- > 0 x - 2 \/ x - 2 \/ x - 2
$$- \sqrt[4]{\frac{12 x}{x - 2}} + \left(\frac{6 x}{x - 2} - \sqrt{\frac{12 x}{x - 2}}\right) > 0$$
-((12*x)/(x - 2))^(1/4) + (6*x)/(x - 2) - sqrt((12*x)/(x - 2)) > 0
Solución detallada
Se da la desigualdad:
$$- \sqrt[4]{\frac{12 x}{x - 2}} + \left(\frac{6 x}{x - 2} - \sqrt{\frac{12 x}{x - 2}}\right) > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$- \sqrt[4]{\frac{12 x}{x - 2}} + \left(\frac{6 x}{x - 2} - \sqrt{\frac{12 x}{x - 2}}\right) = 0$$
Resolvemos:
$$x_{1} = 0$$
$$x_{2} = \frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}$$
$$x_{1} = 0$$
$$x_{2} = \frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}$$
Las raíces dadas
$$x_{2} = \frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}$$
$$x_{1} = 0$$
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
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} + - \frac{1}{10}$$
=
$$\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}$$
lo sustituimos en la expresión
$$- \sqrt[4]{\frac{12 x}{x - 2}} + \left(\frac{6 x}{x - 2} - \sqrt{\frac{12 x}{x - 2}}\right) > 0$$
$$- \sqrt[4]{\frac{12 \left(\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}\right)}{\left(\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}\right) - 2}} + \left(- \sqrt{\frac{12 \left(\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}\right)}{\left(\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}\right) - 2}} + \frac{6 \left(\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}\right)}{\left(\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}\right) - 2}\right) > 0$$
significa que una de las soluciones de nuestra ecuación será con:
$$x < \frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < \frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}$$
$$x > 0$$
$$- \sqrt[4]{\frac{12 x}{x - 2}} + \left(\frac{6 x}{x - 2} - \sqrt{\frac{12 x}{x - 2}}\right) > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$- \sqrt[4]{\frac{12 x}{x - 2}} + \left(\frac{6 x}{x - 2} - \sqrt{\frac{12 x}{x - 2}}\right) = 0$$
Resolvemos:
$$x_{1} = 0$$
$$x_{2} = \frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}$$
$$x_{1} = 0$$
$$x_{2} = \frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}$$
Las raíces dadas
$$x_{2} = \frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}$$
$$x_{1} = 0$$
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
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} + - \frac{1}{10}$$
=
$$\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}$$
lo sustituimos en la expresión
$$- \sqrt[4]{\frac{12 x}{x - 2}} + \left(\frac{6 x}{x - 2} - \sqrt{\frac{12 x}{x - 2}}\right) > 0$$
$$- \sqrt[4]{\frac{12 \left(\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}\right)}{\left(\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}\right) - 2}} + \left(- \sqrt{\frac{12 \left(\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}\right)}{\left(\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}\right) - 2}} + \frac{6 \left(\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}\right)}{\left(\frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}} - \frac{1}{10}\right) - 2}\right) > 0$$
4
/ ___________________________ \
| / ___ 4 ___ 3/4 ____ ___ |
| / \/ 2 *\/ 3 3 *\/ 38 \/ 3 |
12*|3 / ----------- + ----------- + ----------------------------------|
|\/ 12 108 ___________________________|
| / ___ 4 ___ 3/4 ____ |
| / \/ 2 *\/ 3 3 *\/ 38 |
| 9*3 / ----------- + ----------- |
3 \ \/ 12 108 /
- - + ----------------------------------------------------------------------------- ___________________________________________________________________________________ ___________________________________________________________________________________
5 4 / 4 / 4
/ ___________________________ \ / / ___________________________ \ / / ___________________________ \
| / ___ 4 ___ 3/4 ____ ___ | / | / ___ 4 ___ 3/4 ____ ___ | / | / ___ 4 ___ 3/4 ____ ___ |
| / \/ 2 *\/ 3 3 *\/ 38 \/ 3 | / | / \/ 2 *\/ 3 3 *\/ 38 \/ 3 | / | / \/ 2 *\/ 3 3 *\/ 38 \/ 3 |
-1 + |3 / ----------- + ----------- + ----------------------------------| / 24*|3 / ----------- + ----------- + ----------------------------------| / 24*|3 / ----------- + ----------- + ----------------------------------|
|\/ 12 108 ___________________________| / |\/ 12 108 ___________________________| / |\/ 12 108 ___________________________|
| / ___ 4 ___ 3/4 ____ | / | / ___ 4 ___ 3/4 ____ | / | / ___ 4 ___ 3/4 ____ |
| / \/ 2 *\/ 3 3 *\/ 38 | / | / \/ 2 *\/ 3 3 *\/ 38 | / | / \/ 2 *\/ 3 3 *\/ 38 |
| 9*3 / ----------- + ----------- | ______________________________________________________________________________________ / | 9*3 / ----------- + ----------- | ______________________________________________________________________________________ / | 9*3 / ----------- + ----------- |
\ \/ 12 108 / / -1 / 6 \ \/ 12 108 / / -1 / 6 \ \/ 12 108 /
------------------------------------------------------------------------------------ - / ------------------------------------------------------------------------------------ * / - - ----------------------------------------------------------------------------- - / ------------------------------------------------------------------------------------ * / - - ----------------------------------------------------------------------------- > 0
4 / 4 / 5 4 / 4 / 5 4
/ ___________________________ \ / / ___________________________ \ / / ___________________________ \ / / ___________________________ \ / / ___________________________ \
| / ___ 4 ___ 3/4 ____ ___ | / | / ___ 4 ___ 3/4 ____ ___ | / | / ___ 4 ___ 3/4 ____ ___ | / | / ___ 4 ___ 3/4 ____ ___ | / | / ___ 4 ___ 3/4 ____ ___ |
| / \/ 2 *\/ 3 3 *\/ 38 \/ 3 | / | / \/ 2 *\/ 3 3 *\/ 38 \/ 3 | / | / \/ 2 *\/ 3 3 *\/ 38 \/ 3 | / | / \/ 2 *\/ 3 3 *\/ 38 \/ 3 | / | / \/ 2 *\/ 3 3 *\/ 38 \/ 3 |
2*|3 / ----------- + ----------- + ----------------------------------| / 2*|3 / ----------- + ----------- + ----------------------------------| / -1 + |3 / ----------- + ----------- + ----------------------------------| / 2*|3 / ----------- + ----------- + ----------------------------------| / -1 + |3 / ----------- + ----------- + ----------------------------------|
|\/ 12 108 ___________________________| / |\/ 12 108 ___________________________| / |\/ 12 108 ___________________________| / |\/ 12 108 ___________________________| / |\/ 12 108 ___________________________|
| / ___ 4 ___ 3/4 ____ | / | / ___ 4 ___ 3/4 ____ | / | / ___ 4 ___ 3/4 ____ | / | / ___ 4 ___ 3/4 ____ | / | / ___ 4 ___ 3/4 ____ |
| / \/ 2 *\/ 3 3 *\/ 38 | / | / \/ 2 *\/ 3 3 *\/ 38 | / | / \/ 2 *\/ 3 3 *\/ 38 | / | / \/ 2 *\/ 3 3 *\/ 38 | / | / \/ 2 *\/ 3 3 *\/ 38 |
| 9*3 / ----------- + ----------- | / | 9*3 / ----------- + ----------- | / | 9*3 / ----------- + ----------- | / | 9*3 / ----------- + ----------- | 4 / | 9*3 / ----------- + ----------- |
21 \ \/ 12 108 / / 21 \ \/ 12 108 / \/ \ \/ 12 108 / / 21 \ \/ 12 108 / \/ \ \/ 12 108 /
- -- + ----------------------------------------------------------------------------- / - -- + ----------------------------------------------------------------------------- / - -- + -----------------------------------------------------------------------------
10 4 / 10 4 / 10 4
/ ___________________________ \ / / ___________________________ \ / / ___________________________ \
| / ___ 4 ___ 3/4 ____ ___ | / | / ___ 4 ___ 3/4 ____ ___ | / | / ___ 4 ___ 3/4 ____ ___ |
| / \/ 2 *\/ 3 3 *\/ 38 \/ 3 | / | / \/ 2 *\/ 3 3 *\/ 38 \/ 3 | / | / \/ 2 *\/ 3 3 *\/ 38 \/ 3 |
-1 + |3 / ----------- + ----------- + ----------------------------------| / -1 + |3 / ----------- + ----------- + ----------------------------------| / -1 + |3 / ----------- + ----------- + ----------------------------------|
|\/ 12 108 ___________________________| / |\/ 12 108 ___________________________| / |\/ 12 108 ___________________________|
| / ___ 4 ___ 3/4 ____ | / | / ___ 4 ___ 3/4 ____ | / | / ___ 4 ___ 3/4 ____ |
| / \/ 2 *\/ 3 3 *\/ 38 | / | / \/ 2 *\/ 3 3 *\/ 38 | / | / \/ 2 *\/ 3 3 *\/ 38 |
| 9*3 / ----------- + ----------- | / | 9*3 / ----------- + ----------- | 4 / | 9*3 / ----------- + ----------- |
\ \/ 12 108 / \/ \ \/ 12 108 / \/ \ \/ 12 108 / significa que una de las soluciones de nuestra ecuación será con:
$$x < \frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}$$
_____ _____
\ /
-------ο-------ο-------
x2 x1Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < \frac{2 \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}{-1 + \left(\frac{\sqrt{3}}{9 \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}} + \sqrt[3]{\frac{2^{\frac{3}{4}} \cdot 3 \sqrt{38} \sqrt[4]{54}}{648} + \frac{\sqrt{2} \sqrt[4]{3}}{12}}\right)^{4}}$$
$$x > 0$$
Solución de la desigualdad en el gráfico