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- Desigualdades:
-
x^2>1
-
(x-2)/(x-4)>0
-
x+1>0
- (x-7)(x+8)>0
-
Expresiones idénticas
- sqrt(3x+5x+ siete)-sqrt(3x^ dos +5x+ dos)> uno
- raíz cuadrada de (3x más 5x más 7) menos raíz cuadrada de (3x al cuadrado más 5x más 2) más 1
- raíz cuadrada de (3x más 5x más siete) menos raíz cuadrada de (3x en el grado dos más 5x más dos) más uno
- √(3x+5x+7)-√(3x^2+5x+2)>1
- sqrt(3x+5x+7)-sqrt(3x2+5x+2)>1
- sqrt3x+5x+7-sqrt3x2+5x+2>1
- sqrt(3x+5x+7)-sqrt(3x²+5x+2)>1
- sqrt(3x+5x+7)-sqrt(3x en el grado 2+5x+2)>1
- sqrt3x+5x+7-sqrt3x^2+5x+2>1
-
Expresiones semejantes
- sqrt(3x+5x+7)-sqrt(3x^2-5x+2)>1
- sqrt(3x+5x-7)-sqrt(3x^2+5x+2)>1
- sqrt(3x+5x+7)+sqrt(3x^2+5x+2)>1
- sqrt(3x-5x+7)-sqrt(3x^2+5x+2)>1
- sqrt(3x+5x+7)-sqrt(3x^2+5x-2)>1
-
Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x^2-x-12)>=x
- sqrt(x-2)>x-3
- sqrt(x^2+x-3)>3
- sqrt(x)<5
- sqrt(x-4)<1
- Raíz cuadrada sqrt
- sqrt(x^2-x-12)>=x
- sqrt(x-2)>x-3
- sqrt(x^2+x-3)>3
- sqrt(x)<5
- sqrt(x-4)<1
sqrt(3x+5x+7)-sqrt(3x^2+5x+2)>1 desigualdades
Solución
Ha introducido
[src]
________________ _______________ / 2 \/ 3*x + 5*x + 7 - \/ 3*x + 5*x + 2 > 1
$$\sqrt{\left(3 x + 5 x\right) + 7} - \sqrt{\left(3 x^{2} + 5 x\right) + 2} > 1$$
sqrt(3*x + 5*x + 7) - sqrt(3*x^2 + 5*x + 2) > 1
Solución detallada
Se da la desigualdad:
$$\sqrt{\left(3 x + 5 x\right) + 7} - \sqrt{\left(3 x^{2} + 5 x\right) + 2} > 1$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\sqrt{\left(3 x + 5 x\right) + 7} - \sqrt{\left(3 x^{2} + 5 x\right) + 2} = 1$$
Resolvemos:
$$x_{1} = - \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2} + \frac{1}{2} - \frac{\sqrt{- \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} - 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 6}}{2}$$
$$x_{2} = - \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2} + \frac{1}{2} + \frac{\sqrt{- \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} - 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 6}}{2}$$
$$x_{3} = - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{1}{2} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}$$
Descartamos las soluciones complejas:
$$x_{1} = - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{1}{2} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}$$
Las raíces dadas
$$x_{1} = - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{1}{2} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{1}{2} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}\right)$$
=
$$- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{2}{5} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}$$
lo sustituimos en la expresión
$$\sqrt{\left(3 x + 5 x\right) + 7} - \sqrt{\left(3 x^{2} + 5 x\right) + 2} > 1$$
$$- \sqrt{2 + \left(3 \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{2}{5} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}\right)^{2} + 5 \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{2}{5} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}\right)\right)} + \sqrt{\left(3 \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{2}{5} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}\right) + 5 \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{2}{5} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}\right)\right) + 7} > 1$$
significa que la solución de la desigualdad será con:
$$x < - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{1}{2} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}$$
$$\sqrt{\left(3 x + 5 x\right) + 7} - \sqrt{\left(3 x^{2} + 5 x\right) + 2} > 1$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\sqrt{\left(3 x + 5 x\right) + 7} - \sqrt{\left(3 x^{2} + 5 x\right) + 2} = 1$$
Resolvemos:
$$x_{1} = - \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2} + \frac{1}{2} - \frac{\sqrt{- \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} - 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 6}}{2}$$
$$x_{2} = - \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2} + \frac{1}{2} + \frac{\sqrt{- \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} - 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 6}}{2}$$
$$x_{3} = - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{1}{2} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}$$
Descartamos las soluciones complejas:
$$x_{1} = - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{1}{2} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}$$
Las raíces dadas
$$x_{1} = - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{1}{2} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{1}{2} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}\right)$$
=
$$- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{2}{5} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}$$
lo sustituimos en la expresión
$$\sqrt{\left(3 x + 5 x\right) + 7} - \sqrt{\left(3 x^{2} + 5 x\right) + 2} > 1$$
$$- \sqrt{2 + \left(3 \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{2}{5} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}\right)^{2} + 5 \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{2}{5} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}\right)\right)} + \sqrt{\left(3 \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{2}{5} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}\right) + 5 \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{2}{5} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}\right)\right) + 7} > 1$$
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
/ 2
/ / ___________________________________________________________________________________________________________________________\ ___________________________________________________________________________________________________________________________
/ | / _______________ | / _______________
/ | / / _____ | / / _____
/ | / / 323 \/ 573 67 64 | / / 323 \/ 573 67 64
/ | / 6 - 2*3 / --- + ------- - ----------------------- + ------------------------------------------------------------------ | 5* / 6 - 2*3 / --- + ------- - ----------------------- + ------------------------------------------------------------------
/ | ______________________________________________________ / \/ 648 243 _______________ ______________________________________________________ | / \/ 648 243 _______________ ______________________________________________________ ______________________________________________________
/ | / _______________ / / _____ / _______________ | / / _____ / _______________ / _______________
/ | / / _____ / / 323 \/ 573 / / _____ | / / 323 \/ 573 / / _____ / / _____
/ | / / 323 \/ 573 67 / 54*3 / --- + ------- / / 323 \/ 573 67 | / 54*3 / --- + ------- / / 323 \/ 573 67 / / 323 \/ 573 67
/ | / 3 + 2*3 / --- + ------- + ----------------------- / \/ 648 243 9* / 3 + 2*3 / --- + ------- + ----------------------- | / \/ 648 243 9* / 3 + 2*3 / --- + ------- + ----------------------- 5* / 3 + 2*3 / --- + ------- + -----------------------
________________________________________________________________________________________________________________________________________________________________________________________________________________________ / | / \/ 648 243 _______________ / / \/ 648 243 _______________ | / / \/ 648 243 _______________ / \/ 648 243 _______________
/ ___________________________________________________________________________________________________________________________ ______________________________________________________ / | / / _____ / / / _____ | / / / _____ / / _____
/ / _______________ / _______________ / | / / 323 \/ 573 / / / 323 \/ 573 | / / / 323 \/ 573 / / 323 \/ 573 > 1
/ / / _____ / / _____ / | / 54*3 / --- + ------- / / 54*3 / --- + ------- | / / 54*3 / --- + ------- / 54*3 / --- + -------
/ 51 / / 323 \/ 573 67 64 / / 323 \/ 573 67 / |2 \/ \/ 648 243 \/ \/ \/ 648 243 | \/ \/ \/ 648 243 \/ \/ 648 243
/ -- - 4* / 6 - 2*3 / --- + ------- - ----------------------- + ------------------------------------------------------------------ + 4* / 3 + 2*3 / --- + ------- + ----------------------- - / 4 + 3*|- + ---------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------| - -------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------
/ 5 / \/ 648 243 _______________ ______________________________________________________ / \/ 648 243 _______________ \/ \5 2 2 / 2 2
/ / / _____ / _______________ / / _____
/ / / 323 \/ 573 / / _____ / / 323 \/ 573
/ / 54*3 / --- + ------- / / 323 \/ 573 67 / 54*3 / --- + -------
/ / \/ 648 243 9* / 3 + 2*3 / --- + ------- + ----------------------- \/ \/ 648 243
/ / / \/ 648 243 _______________
/ / / / _____
/ / / / 323 \/ 573
/ / / 54*3 / --- + -------
\/ \/ \/ \/ 648 243
significa que la solución de la desigualdad será con:
$$x < - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} - \frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + \frac{64}{9 \sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}} + 6}}{2} + \frac{1}{2} + \frac{\sqrt{\frac{67}{54 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}}} + 2 \sqrt[3]{\frac{\sqrt{573}}{243} + \frac{323}{648}} + 3}}{2}$$
_____
\
-------ο-------
x1
Solución de la desigualdad en el gráfico
Respuesta rápida
[src]
/ __________________________________________________________________________________________________________________________ \ | / _________________ 2/3 | | / 192 3 ___ 3 / _____ 67*3 | | / 54 + --------------------------------------------------------------- - \/ 3 *\/ 969 + 8*\/ 573 - -------------------- | | / ________________________________________________________ _________________ ________________________________________________________| | / / _________________ 2/3 3 / _____ / _________________ 2/3 | | / / 3 ___ 3 / _____ 67*3 \/ 969 + 8*\/ 573 / 3 ___ 3 / _____ 67*3 | | / / 27 + \/ 3 *\/ 969 + 8*\/ 573 + -------------------- / 27 + \/ 3 *\/ 969 + 8*\/ 573 + -------------------- | | / / _________________ / _________________ | | / / 3 / _____ / 3 / _____ | | 1 \/ \/ \/ 969 + 8*\/ 573 \/ \/ 969 + 8*\/ 573 | And|-2/3 <= x, x < - - ------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------| \ 2 6 6 /
$$- \frac{2}{3} \leq x \wedge x < - \frac{\sqrt{- \sqrt[3]{3} \sqrt[3]{8 \sqrt{573} + 969} - \frac{67 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{8 \sqrt{573} + 969}} + \frac{192}{\sqrt{\frac{67 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{8 \sqrt{573} + 969}} + \sqrt[3]{3} \sqrt[3]{8 \sqrt{573} + 969} + 27}} + 54}}{6} + \frac{1}{2} + \frac{\sqrt{\frac{67 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{8 \sqrt{573} + 969}} + \sqrt[3]{3} \sqrt[3]{8 \sqrt{573} + 969} + 27}}{6}$$
(-2/3 <= x)∧(x < 1/2 - sqrt(54 + 192/sqrt(27 + 3^(1/3)*(969 + 8*sqrt(573))^(1/3) + 67*3^(2/3)/(969 + 8*sqrt(573))^(1/3)) - 3^(1/3)*(969 + 8*sqrt(573))^(1/3) - 67*3^(2/3)/(969 + 8*sqrt(573))^(1/3))/6 + sqrt(27 + 3^(1/3)*(969 + 8*sqrt(573))^(1/3) + 67*3^(2/3)/(969 + 8*sqrt(573))^(1/3))/6)
Respuesta rápida 2
[src]
__________________________________________________________________________________________________________________________
/ _________________ 2/3
/ 192 3 ___ 3 / _____ 67*3
/ 54 + --------------------------------------------------------------- - \/ 3 *\/ 969 + 8*\/ 573 - --------------------
/ ________________________________________________________ _________________ ________________________________________________________
/ / _________________ 2/3 3 / _____ / _________________ 2/3
/ / 3 ___ 3 / _____ 67*3 \/ 969 + 8*\/ 573 / 3 ___ 3 / _____ 67*3
/ / 27 + \/ 3 *\/ 969 + 8*\/ 573 + -------------------- / 27 + \/ 3 *\/ 969 + 8*\/ 573 + --------------------
/ / _________________ / _________________
/ / 3 / _____ / 3 / _____
1 \/ \/ \/ 969 + 8*\/ 573 \/ \/ 969 + 8*\/ 573
[-2/3, - - ------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------)
2 6 6
$$x\ in\ \left[- \frac{2}{3}, - \frac{\sqrt{- \sqrt[3]{3} \sqrt[3]{8 \sqrt{573} + 969} - \frac{67 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{8 \sqrt{573} + 969}} + \frac{192}{\sqrt{\frac{67 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{8 \sqrt{573} + 969}} + \sqrt[3]{3} \sqrt[3]{8 \sqrt{573} + 969} + 27}} + 54}}{6} + \frac{1}{2} + \frac{\sqrt{\frac{67 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{8 \sqrt{573} + 969}} + \sqrt[3]{3} \sqrt[3]{8 \sqrt{573} + 969} + 27}}{6}\right)$$
x in Interval.Ropen(-2/3, -sqrt(-3^(1/3)*(8*sqrt(573) + 969)^(1/3) - 67*3^(2/3)/(8*sqrt(573) + 969)^(1/3) + 192/sqrt(67*3^(2/3)/(8*sqrt(573) + 969)^(1/3) + 3^(1/3)*(8*sqrt(573) + 969)^(1/3) + 27) + 54)/6 + 1/2 + sqrt(67*3^(2/3)/(8*sqrt(573) + 969)^(1/3) + 3^(1/3)*(8*sqrt(573) + 969)^(1/3) + 27)/6)