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-
¿Cómo usar?
- Desigualdades:
-
x^2-4x+3<0
-
x^2-3x+2<0
-
-x^2+x+6>0
-
-x^2-x+12>0
-
Expresiones idénticas
- nueve ^x+ dos * seis ^x- tres * cuatro ^x> cero
- 9 en el grado x más 2 multiplicar por 6 en el grado x menos 3 multiplicar por 4 en el grado x más 0
- nueve en el grado x más dos multiplicar por seis en el grado x menos tres multiplicar por cuatro en el grado x más cero
- 9x+2*6x-3*4x>0
- 9^x+26^x-34^x>0
- 9x+26x-34x>0
-
Expresiones semejantes
- 9^x-2*6^x-3*4^x>0
- 9^x+2*6^x+3*4^x>0
9^x+2*6^x-3*4^x>0 desigualdades
Solución
Ha introducido
[src]
x x x 9 + 2*6 - 3*4 > 0
$$- 3 \cdot 4^{x} + \left(2 \cdot 6^{x} + 9^{x}\right) > 0$$
-3*4^x + 2*6^x + 9^x > 0
Solución detallada
Se da la desigualdad:
$$- 3 \cdot 4^{x} + \left(2 \cdot 6^{x} + 9^{x}\right) > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$- 3 \cdot 4^{x} + \left(2 \cdot 6^{x} + 9^{x}\right) = 0$$
Resolvemos:
$$x_{1} = -69.0161482957947$$
$$x_{2} = -45.0161513532851$$
$$x_{3} = -85.0161482956133$$
$$x_{4} = -109.016148295613$$
$$x_{5} = -71.0161482956938$$
$$x_{6} = -75.016148295629$$
$$x_{7} = -111.016148295613$$
$$x_{8} = -91.0161482956131$$
$$x_{9} = -55.0161483486375$$
$$x_{10} = -47.0161496545744$$
$$x_{11} = -89.0161482956131$$
$$x_{12} = -115.016148295613$$
$$x_{13} = -29.0181637990876$$
$$x_{14} = -103.016148295613$$
$$x_{15} = -21.0726174334674$$
$$x_{16} = -67.0161482960218$$
$$x_{17} = -43.0161551754213$$
$$x_{18} = -81.0161482956145$$
$$x_{19} = -113.016148295613$$
$$x_{20} = -37.0162266707795$$
$$x_{21} = -97.0161482956131$$
$$x_{22} = -53.0161484149181$$
$$x_{23} = -33.016545292091$$
$$x_{24} = -41.0161637754157$$
$$x_{25} = -73.0161482956489$$
$$x_{26} = -83.0161482956137$$
$$x_{27} = -61.0161483002682$$
$$x_{28} = -107.016148295613$$
$$x_{29} = -95.0161482956131$$
$$x_{30} = -39.016183126354$$
$$x_{31} = -31.0170423172624$$
$$x_{32} = -57.0161483191795$$
$$x_{33} = 0$$
$$x_{34} = -59.016148306087$$
$$x_{35} = -35.016324670115$$
$$x_{36} = -63.016148297682$$
$$x_{37} = -105.016148295613$$
$$x_{38} = -51.0161485640494$$
$$x_{39} = -25.0264999570366$$
$$x_{40} = -87.0161482956132$$
$$x_{41} = -101.016148295613$$
$$x_{42} = -79.0161482956162$$
$$x_{43} = -49.0161488995951$$
$$x_{44} = -77.0161482956202$$
$$x_{45} = -23.0399734010519$$
$$x_{46} = -27.0207032931812$$
$$x_{47} = -99.0161482956131$$
$$x_{48} = -65.0161482965326$$
$$x_{49} = -93.0161482956131$$
$$x_{1} = -69.0161482957947$$
$$x_{2} = -45.0161513532851$$
$$x_{3} = -85.0161482956133$$
$$x_{4} = -109.016148295613$$
$$x_{5} = -71.0161482956938$$
$$x_{6} = -75.016148295629$$
$$x_{7} = -111.016148295613$$
$$x_{8} = -91.0161482956131$$
$$x_{9} = -55.0161483486375$$
$$x_{10} = -47.0161496545744$$
$$x_{11} = -89.0161482956131$$
$$x_{12} = -115.016148295613$$
$$x_{13} = -29.0181637990876$$
$$x_{14} = -103.016148295613$$
$$x_{15} = -21.0726174334674$$
$$x_{16} = -67.0161482960218$$
$$x_{17} = -43.0161551754213$$
$$x_{18} = -81.0161482956145$$
$$x_{19} = -113.016148295613$$
$$x_{20} = -37.0162266707795$$
$$x_{21} = -97.0161482956131$$
$$x_{22} = -53.0161484149181$$
$$x_{23} = -33.016545292091$$
$$x_{24} = -41.0161637754157$$
$$x_{25} = -73.0161482956489$$
$$x_{26} = -83.0161482956137$$
$$x_{27} = -61.0161483002682$$
$$x_{28} = -107.016148295613$$
$$x_{29} = -95.0161482956131$$
$$x_{30} = -39.016183126354$$
$$x_{31} = -31.0170423172624$$
$$x_{32} = -57.0161483191795$$
$$x_{33} = 0$$
$$x_{34} = -59.016148306087$$
$$x_{35} = -35.016324670115$$
$$x_{36} = -63.016148297682$$
$$x_{37} = -105.016148295613$$
$$x_{38} = -51.0161485640494$$
$$x_{39} = -25.0264999570366$$
$$x_{40} = -87.0161482956132$$
$$x_{41} = -101.016148295613$$
$$x_{42} = -79.0161482956162$$
$$x_{43} = -49.0161488995951$$
$$x_{44} = -77.0161482956202$$
$$x_{45} = -23.0399734010519$$
$$x_{46} = -27.0207032931812$$
$$x_{47} = -99.0161482956131$$
$$x_{48} = -65.0161482965326$$
$$x_{49} = -93.0161482956131$$
Las raíces dadas
$$x_{12} = -115.016148295613$$
$$x_{19} = -113.016148295613$$
$$x_{7} = -111.016148295613$$
$$x_{4} = -109.016148295613$$
$$x_{28} = -107.016148295613$$
$$x_{37} = -105.016148295613$$
$$x_{14} = -103.016148295613$$
$$x_{41} = -101.016148295613$$
$$x_{47} = -99.0161482956131$$
$$x_{21} = -97.0161482956131$$
$$x_{29} = -95.0161482956131$$
$$x_{49} = -93.0161482956131$$
$$x_{8} = -91.0161482956131$$
$$x_{11} = -89.0161482956131$$
$$x_{40} = -87.0161482956132$$
$$x_{3} = -85.0161482956133$$
$$x_{26} = -83.0161482956137$$
$$x_{18} = -81.0161482956145$$
$$x_{42} = -79.0161482956162$$
$$x_{44} = -77.0161482956202$$
$$x_{6} = -75.016148295629$$
$$x_{25} = -73.0161482956489$$
$$x_{5} = -71.0161482956938$$
$$x_{1} = -69.0161482957947$$
$$x_{16} = -67.0161482960218$$
$$x_{48} = -65.0161482965326$$
$$x_{36} = -63.016148297682$$
$$x_{27} = -61.0161483002682$$
$$x_{34} = -59.016148306087$$
$$x_{32} = -57.0161483191795$$
$$x_{9} = -55.0161483486375$$
$$x_{22} = -53.0161484149181$$
$$x_{38} = -51.0161485640494$$
$$x_{43} = -49.0161488995951$$
$$x_{10} = -47.0161496545744$$
$$x_{2} = -45.0161513532851$$
$$x_{17} = -43.0161551754213$$
$$x_{24} = -41.0161637754157$$
$$x_{30} = -39.016183126354$$
$$x_{20} = -37.0162266707795$$
$$x_{35} = -35.016324670115$$
$$x_{23} = -33.016545292091$$
$$x_{31} = -31.0170423172624$$
$$x_{13} = -29.0181637990876$$
$$x_{46} = -27.0207032931812$$
$$x_{39} = -25.0264999570366$$
$$x_{45} = -23.0399734010519$$
$$x_{15} = -21.0726174334674$$
$$x_{33} = 0$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{12}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{12} - \frac{1}{10}$$
=
$$-115.016148295613 + - \frac{1}{10}$$
=
$$-115.116148295613$$
lo sustituimos en la expresión
$$- 3 \cdot 4^{x} + \left(2 \cdot 6^{x} + 9^{x}\right) > 0$$
$$- \frac{3}{4^{115.116148295613}} + \left(9^{-115.116148295613} + \frac{2}{6^{115.116148295613}}\right) > 0$$
Entonces
$$x < -115.016148295613$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -115.016148295613 \wedge x < -113.016148295613$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -115.016148295613 \wedge x < -113.016148295613$$
$$x > -111.016148295613 \wedge x < -109.016148295613$$
$$x > -107.016148295613 \wedge x < -105.016148295613$$
$$x > -103.016148295613 \wedge x < -101.016148295613$$
$$x > -99.0161482956131 \wedge x < -97.0161482956131$$
$$x > -95.0161482956131 \wedge x < -93.0161482956131$$
$$x > -91.0161482956131 \wedge x < -89.0161482956131$$
$$x > -87.0161482956132 \wedge x < -85.0161482956133$$
$$x > -83.0161482956137 \wedge x < -81.0161482956145$$
$$x > -79.0161482956162 \wedge x < -77.0161482956202$$
$$x > -75.016148295629 \wedge x < -73.0161482956489$$
$$x > -71.0161482956938 \wedge x < -69.0161482957947$$
$$x > -67.0161482960218 \wedge x < -65.0161482965326$$
$$x > -63.016148297682 \wedge x < -61.0161483002682$$
$$x > -59.016148306087 \wedge x < -57.0161483191795$$
$$x > -55.0161483486375 \wedge x < -53.0161484149181$$
$$x > -51.0161485640494 \wedge x < -49.0161488995951$$
$$x > -47.0161496545744 \wedge x < -45.0161513532851$$
$$x > -43.0161551754213 \wedge x < -41.0161637754157$$
$$x > -39.016183126354 \wedge x < -37.0162266707795$$
$$x > -35.016324670115 \wedge x < -33.016545292091$$
$$x > -31.0170423172624 \wedge x < -29.0181637990876$$
$$x > -27.0207032931812 \wedge x < -25.0264999570366$$
$$x > -23.0399734010519 \wedge x < -21.0726174334674$$
$$x > 0$$
$$- 3 \cdot 4^{x} + \left(2 \cdot 6^{x} + 9^{x}\right) > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$- 3 \cdot 4^{x} + \left(2 \cdot 6^{x} + 9^{x}\right) = 0$$
Resolvemos:
$$x_{1} = -69.0161482957947$$
$$x_{2} = -45.0161513532851$$
$$x_{3} = -85.0161482956133$$
$$x_{4} = -109.016148295613$$
$$x_{5} = -71.0161482956938$$
$$x_{6} = -75.016148295629$$
$$x_{7} = -111.016148295613$$
$$x_{8} = -91.0161482956131$$
$$x_{9} = -55.0161483486375$$
$$x_{10} = -47.0161496545744$$
$$x_{11} = -89.0161482956131$$
$$x_{12} = -115.016148295613$$
$$x_{13} = -29.0181637990876$$
$$x_{14} = -103.016148295613$$
$$x_{15} = -21.0726174334674$$
$$x_{16} = -67.0161482960218$$
$$x_{17} = -43.0161551754213$$
$$x_{18} = -81.0161482956145$$
$$x_{19} = -113.016148295613$$
$$x_{20} = -37.0162266707795$$
$$x_{21} = -97.0161482956131$$
$$x_{22} = -53.0161484149181$$
$$x_{23} = -33.016545292091$$
$$x_{24} = -41.0161637754157$$
$$x_{25} = -73.0161482956489$$
$$x_{26} = -83.0161482956137$$
$$x_{27} = -61.0161483002682$$
$$x_{28} = -107.016148295613$$
$$x_{29} = -95.0161482956131$$
$$x_{30} = -39.016183126354$$
$$x_{31} = -31.0170423172624$$
$$x_{32} = -57.0161483191795$$
$$x_{33} = 0$$
$$x_{34} = -59.016148306087$$
$$x_{35} = -35.016324670115$$
$$x_{36} = -63.016148297682$$
$$x_{37} = -105.016148295613$$
$$x_{38} = -51.0161485640494$$
$$x_{39} = -25.0264999570366$$
$$x_{40} = -87.0161482956132$$
$$x_{41} = -101.016148295613$$
$$x_{42} = -79.0161482956162$$
$$x_{43} = -49.0161488995951$$
$$x_{44} = -77.0161482956202$$
$$x_{45} = -23.0399734010519$$
$$x_{46} = -27.0207032931812$$
$$x_{47} = -99.0161482956131$$
$$x_{48} = -65.0161482965326$$
$$x_{49} = -93.0161482956131$$
$$x_{1} = -69.0161482957947$$
$$x_{2} = -45.0161513532851$$
$$x_{3} = -85.0161482956133$$
$$x_{4} = -109.016148295613$$
$$x_{5} = -71.0161482956938$$
$$x_{6} = -75.016148295629$$
$$x_{7} = -111.016148295613$$
$$x_{8} = -91.0161482956131$$
$$x_{9} = -55.0161483486375$$
$$x_{10} = -47.0161496545744$$
$$x_{11} = -89.0161482956131$$
$$x_{12} = -115.016148295613$$
$$x_{13} = -29.0181637990876$$
$$x_{14} = -103.016148295613$$
$$x_{15} = -21.0726174334674$$
$$x_{16} = -67.0161482960218$$
$$x_{17} = -43.0161551754213$$
$$x_{18} = -81.0161482956145$$
$$x_{19} = -113.016148295613$$
$$x_{20} = -37.0162266707795$$
$$x_{21} = -97.0161482956131$$
$$x_{22} = -53.0161484149181$$
$$x_{23} = -33.016545292091$$
$$x_{24} = -41.0161637754157$$
$$x_{25} = -73.0161482956489$$
$$x_{26} = -83.0161482956137$$
$$x_{27} = -61.0161483002682$$
$$x_{28} = -107.016148295613$$
$$x_{29} = -95.0161482956131$$
$$x_{30} = -39.016183126354$$
$$x_{31} = -31.0170423172624$$
$$x_{32} = -57.0161483191795$$
$$x_{33} = 0$$
$$x_{34} = -59.016148306087$$
$$x_{35} = -35.016324670115$$
$$x_{36} = -63.016148297682$$
$$x_{37} = -105.016148295613$$
$$x_{38} = -51.0161485640494$$
$$x_{39} = -25.0264999570366$$
$$x_{40} = -87.0161482956132$$
$$x_{41} = -101.016148295613$$
$$x_{42} = -79.0161482956162$$
$$x_{43} = -49.0161488995951$$
$$x_{44} = -77.0161482956202$$
$$x_{45} = -23.0399734010519$$
$$x_{46} = -27.0207032931812$$
$$x_{47} = -99.0161482956131$$
$$x_{48} = -65.0161482965326$$
$$x_{49} = -93.0161482956131$$
Las raíces dadas
$$x_{12} = -115.016148295613$$
$$x_{19} = -113.016148295613$$
$$x_{7} = -111.016148295613$$
$$x_{4} = -109.016148295613$$
$$x_{28} = -107.016148295613$$
$$x_{37} = -105.016148295613$$
$$x_{14} = -103.016148295613$$
$$x_{41} = -101.016148295613$$
$$x_{47} = -99.0161482956131$$
$$x_{21} = -97.0161482956131$$
$$x_{29} = -95.0161482956131$$
$$x_{49} = -93.0161482956131$$
$$x_{8} = -91.0161482956131$$
$$x_{11} = -89.0161482956131$$
$$x_{40} = -87.0161482956132$$
$$x_{3} = -85.0161482956133$$
$$x_{26} = -83.0161482956137$$
$$x_{18} = -81.0161482956145$$
$$x_{42} = -79.0161482956162$$
$$x_{44} = -77.0161482956202$$
$$x_{6} = -75.016148295629$$
$$x_{25} = -73.0161482956489$$
$$x_{5} = -71.0161482956938$$
$$x_{1} = -69.0161482957947$$
$$x_{16} = -67.0161482960218$$
$$x_{48} = -65.0161482965326$$
$$x_{36} = -63.016148297682$$
$$x_{27} = -61.0161483002682$$
$$x_{34} = -59.016148306087$$
$$x_{32} = -57.0161483191795$$
$$x_{9} = -55.0161483486375$$
$$x_{22} = -53.0161484149181$$
$$x_{38} = -51.0161485640494$$
$$x_{43} = -49.0161488995951$$
$$x_{10} = -47.0161496545744$$
$$x_{2} = -45.0161513532851$$
$$x_{17} = -43.0161551754213$$
$$x_{24} = -41.0161637754157$$
$$x_{30} = -39.016183126354$$
$$x_{20} = -37.0162266707795$$
$$x_{35} = -35.016324670115$$
$$x_{23} = -33.016545292091$$
$$x_{31} = -31.0170423172624$$
$$x_{13} = -29.0181637990876$$
$$x_{46} = -27.0207032931812$$
$$x_{39} = -25.0264999570366$$
$$x_{45} = -23.0399734010519$$
$$x_{15} = -21.0726174334674$$
$$x_{33} = 0$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{12}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{12} - \frac{1}{10}$$
=
$$-115.016148295613 + - \frac{1}{10}$$
=
$$-115.116148295613$$
lo sustituimos en la expresión
$$- 3 \cdot 4^{x} + \left(2 \cdot 6^{x} + 9^{x}\right) > 0$$
$$- \frac{3}{4^{115.116148295613}} + \left(9^{-115.116148295613} + \frac{2}{6^{115.116148295613}}\right) > 0$$
-1.48011005901098e-69 > 0
Entonces
$$x < -115.016148295613$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -115.016148295613 \wedge x < -113.016148295613$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
x12 x19 x7 x4 x28 x37 x14 x41 x47 x21 x29 x49 x8 x11 x40 x3 x26 x18 x42 x44 x6 x25 x5 x1 x16 x48 x36 x27 x34 x32 x9 x22 x38 x43 x10 x2 x17 x24 x30 x20 x35 x23 x31 x13 x46 x39 x45 x15 x33Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -115.016148295613 \wedge x < -113.016148295613$$
$$x > -111.016148295613 \wedge x < -109.016148295613$$
$$x > -107.016148295613 \wedge x < -105.016148295613$$
$$x > -103.016148295613 \wedge x < -101.016148295613$$
$$x > -99.0161482956131 \wedge x < -97.0161482956131$$
$$x > -95.0161482956131 \wedge x < -93.0161482956131$$
$$x > -91.0161482956131 \wedge x < -89.0161482956131$$
$$x > -87.0161482956132 \wedge x < -85.0161482956133$$
$$x > -83.0161482956137 \wedge x < -81.0161482956145$$
$$x > -79.0161482956162 \wedge x < -77.0161482956202$$
$$x > -75.016148295629 \wedge x < -73.0161482956489$$
$$x > -71.0161482956938 \wedge x < -69.0161482957947$$
$$x > -67.0161482960218 \wedge x < -65.0161482965326$$
$$x > -63.016148297682 \wedge x < -61.0161483002682$$
$$x > -59.016148306087 \wedge x < -57.0161483191795$$
$$x > -55.0161483486375 \wedge x < -53.0161484149181$$
$$x > -51.0161485640494 \wedge x < -49.0161488995951$$
$$x > -47.0161496545744 \wedge x < -45.0161513532851$$
$$x > -43.0161551754213 \wedge x < -41.0161637754157$$
$$x > -39.016183126354 \wedge x < -37.0162266707795$$
$$x > -35.016324670115 \wedge x < -33.016545292091$$
$$x > -31.0170423172624 \wedge x < -29.0181637990876$$
$$x > -27.0207032931812 \wedge x < -25.0264999570366$$
$$x > -23.0399734010519 \wedge x < -21.0726174334674$$
$$x > 0$$
Solución de la desigualdad en el gráfico
Gráfico