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-
¿Cómo usar?
- Desigualdades:
-
(x+2)(x^2+x-12)>0
-
(x+5)*(x-4)>0
-
x^2-6x+5<0
-
(x+7)*(x-5)<0
- Forma canónica:
- =0
-
Expresiones idénticas
- nueve ^x+ seis ^x- dos * cuatro ^x<= cero
- 9 en el grado x más 6 en el grado x menos 2 multiplicar por 4 en el grado x menos o igual a 0
- nueve en el grado x más seis en el grado x menos dos multiplicar por cuatro en el grado x menos o igual a cero
- 9x+6x-2*4x<=0
- 9^x+6^x-24^x<=0
- 9x+6x-24x<=0
- 9^x+6^x-2*4^x<=O
-
Expresiones semejantes
- 9^x-6^x-2*4^x<=0
- 9^x+6^x+2*4^x<=0
9^x+6^x-2*4^x<=0 desigualdades
Solución
Ha introducido
[src]
x x x 9 + 6 - 2*4 <= 0
$$- 2 \cdot 4^{x} + \left(6^{x} + 9^{x}\right) \leq 0$$
-2*4^x + 6^x + 9^x <= 0
Solución detallada
Se da la desigualdad:
$$- 2 \cdot 4^{x} + \left(6^{x} + 9^{x}\right) \leq 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$- 2 \cdot 4^{x} + \left(6^{x} + 9^{x}\right) = 0$$
Resolvemos:
$$x_{1} = -45.0161505888731$$
$$x_{2} = -41.0161599056191$$
$$x_{3} = -61.0161482991044$$
$$x_{4} = -83.0161482956135$$
$$x_{5} = -31.0168193242027$$
$$x_{6} = -21.0602579247906$$
$$x_{7} = -109.016148295613$$
$$x_{8} = -79.0161482956154$$
$$x_{9} = -77.0161482956184$$
$$x_{10} = -39.0161744194484$$
$$x_{11} = -89.0161482956131$$
$$x_{12} = -111.016148295613$$
$$x_{13} = -91.0161482956131$$
$$x_{14} = -43.0161534554997$$
$$x_{15} = -115.016148295613$$
$$x_{16} = -37.0162070809351$$
$$x_{17} = -103.016148295613$$
$$x_{18} = -33.0164461441503$$
$$x_{19} = -71.0161482956736$$
$$x_{20} = -113.016148295613$$
$$x_{21} = -59.0161483034685$$
$$x_{22} = -73.01614829564$$
$$x_{23} = -97.0161482956131$$
$$x_{24} = -25.0239788561174$$
$$x_{25} = -81.0161482956141$$
$$x_{26} = -65.0161482963027$$
$$x_{27} = -57.0161483132879$$
$$x_{28} = -85.0161482956133$$
$$x_{29} = -107.016148295613$$
$$x_{30} = -29.0176625185516$$
$$x_{31} = -23.0343578922278$$
$$x_{32} = -95.0161482956131$$
$$x_{33} = -69.0161482957493$$
$$x_{34} = 0$$
$$x_{35} = -47.0161493148352$$
$$x_{36} = -35.0162805964731$$
$$x_{37} = -87.0161482956132$$
$$x_{38} = -53.0161483850918$$
$$x_{39} = -27.0195777004972$$
$$x_{40} = -101.016148295613$$
$$x_{41} = -55.0161483353814$$
$$x_{42} = -63.0161482971648$$
$$x_{43} = -49.0161487485998$$
$$x_{44} = -75.016148295625$$
$$x_{45} = -51.0161484969403$$
$$x_{46} = -67.0161482959196$$
$$x_{47} = -99.0161482956131$$
$$x_{48} = -105.016148295613$$
$$x_{49} = -93.0161482956131$$
$$x_{1} = -45.0161505888731$$
$$x_{2} = -41.0161599056191$$
$$x_{3} = -61.0161482991044$$
$$x_{4} = -83.0161482956135$$
$$x_{5} = -31.0168193242027$$
$$x_{6} = -21.0602579247906$$
$$x_{7} = -109.016148295613$$
$$x_{8} = -79.0161482956154$$
$$x_{9} = -77.0161482956184$$
$$x_{10} = -39.0161744194484$$
$$x_{11} = -89.0161482956131$$
$$x_{12} = -111.016148295613$$
$$x_{13} = -91.0161482956131$$
$$x_{14} = -43.0161534554997$$
$$x_{15} = -115.016148295613$$
$$x_{16} = -37.0162070809351$$
$$x_{17} = -103.016148295613$$
$$x_{18} = -33.0164461441503$$
$$x_{19} = -71.0161482956736$$
$$x_{20} = -113.016148295613$$
$$x_{21} = -59.0161483034685$$
$$x_{22} = -73.01614829564$$
$$x_{23} = -97.0161482956131$$
$$x_{24} = -25.0239788561174$$
$$x_{25} = -81.0161482956141$$
$$x_{26} = -65.0161482963027$$
$$x_{27} = -57.0161483132879$$
$$x_{28} = -85.0161482956133$$
$$x_{29} = -107.016148295613$$
$$x_{30} = -29.0176625185516$$
$$x_{31} = -23.0343578922278$$
$$x_{32} = -95.0161482956131$$
$$x_{33} = -69.0161482957493$$
$$x_{34} = 0$$
$$x_{35} = -47.0161493148352$$
$$x_{36} = -35.0162805964731$$
$$x_{37} = -87.0161482956132$$
$$x_{38} = -53.0161483850918$$
$$x_{39} = -27.0195777004972$$
$$x_{40} = -101.016148295613$$
$$x_{41} = -55.0161483353814$$
$$x_{42} = -63.0161482971648$$
$$x_{43} = -49.0161487485998$$
$$x_{44} = -75.016148295625$$
$$x_{45} = -51.0161484969403$$
$$x_{46} = -67.0161482959196$$
$$x_{47} = -99.0161482956131$$
$$x_{48} = -105.016148295613$$
$$x_{49} = -93.0161482956131$$
Las raíces dadas
$$x_{15} = -115.016148295613$$
$$x_{20} = -113.016148295613$$
$$x_{12} = -111.016148295613$$
$$x_{7} = -109.016148295613$$
$$x_{29} = -107.016148295613$$
$$x_{48} = -105.016148295613$$
$$x_{17} = -103.016148295613$$
$$x_{40} = -101.016148295613$$
$$x_{47} = -99.0161482956131$$
$$x_{23} = -97.0161482956131$$
$$x_{32} = -95.0161482956131$$
$$x_{49} = -93.0161482956131$$
$$x_{13} = -91.0161482956131$$
$$x_{11} = -89.0161482956131$$
$$x_{37} = -87.0161482956132$$
$$x_{28} = -85.0161482956133$$
$$x_{4} = -83.0161482956135$$
$$x_{25} = -81.0161482956141$$
$$x_{8} = -79.0161482956154$$
$$x_{9} = -77.0161482956184$$
$$x_{44} = -75.016148295625$$
$$x_{22} = -73.01614829564$$
$$x_{19} = -71.0161482956736$$
$$x_{33} = -69.0161482957493$$
$$x_{46} = -67.0161482959196$$
$$x_{26} = -65.0161482963027$$
$$x_{42} = -63.0161482971648$$
$$x_{3} = -61.0161482991044$$
$$x_{21} = -59.0161483034685$$
$$x_{27} = -57.0161483132879$$
$$x_{41} = -55.0161483353814$$
$$x_{38} = -53.0161483850918$$
$$x_{45} = -51.0161484969403$$
$$x_{43} = -49.0161487485998$$
$$x_{35} = -47.0161493148352$$
$$x_{1} = -45.0161505888731$$
$$x_{14} = -43.0161534554997$$
$$x_{2} = -41.0161599056191$$
$$x_{10} = -39.0161744194484$$
$$x_{16} = -37.0162070809351$$
$$x_{36} = -35.0162805964731$$
$$x_{18} = -33.0164461441503$$
$$x_{5} = -31.0168193242027$$
$$x_{30} = -29.0176625185516$$
$$x_{39} = -27.0195777004972$$
$$x_{24} = -25.0239788561174$$
$$x_{31} = -23.0343578922278$$
$$x_{6} = -21.0602579247906$$
$$x_{34} = 0$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{15}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{15} - \frac{1}{10}$$
=
$$-115.016148295613 + - \frac{1}{10}$$
=
$$-115.116148295613$$
lo sustituimos en la expresión
$$- 2 \cdot 4^{x} + \left(6^{x} + 9^{x}\right) \leq 0$$
$$- \frac{2}{4^{115.116148295613}} + \left(9^{-115.116148295613} + 6^{-115.116148295613}\right) \leq 0$$
significa que una de las soluciones de nuestra ecuación será con:
$$x \leq -115.016148295613$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \leq -115.016148295613$$
$$x \geq -113.016148295613 \wedge x \leq -111.016148295613$$
$$x \geq -109.016148295613 \wedge x \leq -107.016148295613$$
$$x \geq -105.016148295613 \wedge x \leq -103.016148295613$$
$$x \geq -101.016148295613 \wedge x \leq -99.0161482956131$$
$$x \geq -97.0161482956131 \wedge x \leq -95.0161482956131$$
$$x \geq -93.0161482956131 \wedge x \leq -91.0161482956131$$
$$x \geq -89.0161482956131 \wedge x \leq -87.0161482956132$$
$$x \geq -85.0161482956133 \wedge x \leq -83.0161482956135$$
$$x \geq -81.0161482956141 \wedge x \leq -79.0161482956154$$
$$x \geq -77.0161482956184 \wedge x \leq -75.016148295625$$
$$x \geq -73.01614829564 \wedge x \leq -71.0161482956736$$
$$x \geq -69.0161482957493 \wedge x \leq -67.0161482959196$$
$$x \geq -65.0161482963027 \wedge x \leq -63.0161482971648$$
$$x \geq -61.0161482991044 \wedge x \leq -59.0161483034685$$
$$x \geq -57.0161483132879 \wedge x \leq -55.0161483353814$$
$$x \geq -53.0161483850918 \wedge x \leq -51.0161484969403$$
$$x \geq -49.0161487485998 \wedge x \leq -47.0161493148352$$
$$x \geq -45.0161505888731 \wedge x \leq -43.0161534554997$$
$$x \geq -41.0161599056191 \wedge x \leq -39.0161744194484$$
$$x \geq -37.0162070809351 \wedge x \leq -35.0162805964731$$
$$x \geq -33.0164461441503 \wedge x \leq -31.0168193242027$$
$$x \geq -29.0176625185516 \wedge x \leq -27.0195777004972$$
$$x \geq -25.0239788561174 \wedge x \leq -23.0343578922278$$
$$x \geq -21.0602579247906 \wedge x \leq 0$$
$$- 2 \cdot 4^{x} + \left(6^{x} + 9^{x}\right) \leq 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$- 2 \cdot 4^{x} + \left(6^{x} + 9^{x}\right) = 0$$
Resolvemos:
$$x_{1} = -45.0161505888731$$
$$x_{2} = -41.0161599056191$$
$$x_{3} = -61.0161482991044$$
$$x_{4} = -83.0161482956135$$
$$x_{5} = -31.0168193242027$$
$$x_{6} = -21.0602579247906$$
$$x_{7} = -109.016148295613$$
$$x_{8} = -79.0161482956154$$
$$x_{9} = -77.0161482956184$$
$$x_{10} = -39.0161744194484$$
$$x_{11} = -89.0161482956131$$
$$x_{12} = -111.016148295613$$
$$x_{13} = -91.0161482956131$$
$$x_{14} = -43.0161534554997$$
$$x_{15} = -115.016148295613$$
$$x_{16} = -37.0162070809351$$
$$x_{17} = -103.016148295613$$
$$x_{18} = -33.0164461441503$$
$$x_{19} = -71.0161482956736$$
$$x_{20} = -113.016148295613$$
$$x_{21} = -59.0161483034685$$
$$x_{22} = -73.01614829564$$
$$x_{23} = -97.0161482956131$$
$$x_{24} = -25.0239788561174$$
$$x_{25} = -81.0161482956141$$
$$x_{26} = -65.0161482963027$$
$$x_{27} = -57.0161483132879$$
$$x_{28} = -85.0161482956133$$
$$x_{29} = -107.016148295613$$
$$x_{30} = -29.0176625185516$$
$$x_{31} = -23.0343578922278$$
$$x_{32} = -95.0161482956131$$
$$x_{33} = -69.0161482957493$$
$$x_{34} = 0$$
$$x_{35} = -47.0161493148352$$
$$x_{36} = -35.0162805964731$$
$$x_{37} = -87.0161482956132$$
$$x_{38} = -53.0161483850918$$
$$x_{39} = -27.0195777004972$$
$$x_{40} = -101.016148295613$$
$$x_{41} = -55.0161483353814$$
$$x_{42} = -63.0161482971648$$
$$x_{43} = -49.0161487485998$$
$$x_{44} = -75.016148295625$$
$$x_{45} = -51.0161484969403$$
$$x_{46} = -67.0161482959196$$
$$x_{47} = -99.0161482956131$$
$$x_{48} = -105.016148295613$$
$$x_{49} = -93.0161482956131$$
$$x_{1} = -45.0161505888731$$
$$x_{2} = -41.0161599056191$$
$$x_{3} = -61.0161482991044$$
$$x_{4} = -83.0161482956135$$
$$x_{5} = -31.0168193242027$$
$$x_{6} = -21.0602579247906$$
$$x_{7} = -109.016148295613$$
$$x_{8} = -79.0161482956154$$
$$x_{9} = -77.0161482956184$$
$$x_{10} = -39.0161744194484$$
$$x_{11} = -89.0161482956131$$
$$x_{12} = -111.016148295613$$
$$x_{13} = -91.0161482956131$$
$$x_{14} = -43.0161534554997$$
$$x_{15} = -115.016148295613$$
$$x_{16} = -37.0162070809351$$
$$x_{17} = -103.016148295613$$
$$x_{18} = -33.0164461441503$$
$$x_{19} = -71.0161482956736$$
$$x_{20} = -113.016148295613$$
$$x_{21} = -59.0161483034685$$
$$x_{22} = -73.01614829564$$
$$x_{23} = -97.0161482956131$$
$$x_{24} = -25.0239788561174$$
$$x_{25} = -81.0161482956141$$
$$x_{26} = -65.0161482963027$$
$$x_{27} = -57.0161483132879$$
$$x_{28} = -85.0161482956133$$
$$x_{29} = -107.016148295613$$
$$x_{30} = -29.0176625185516$$
$$x_{31} = -23.0343578922278$$
$$x_{32} = -95.0161482956131$$
$$x_{33} = -69.0161482957493$$
$$x_{34} = 0$$
$$x_{35} = -47.0161493148352$$
$$x_{36} = -35.0162805964731$$
$$x_{37} = -87.0161482956132$$
$$x_{38} = -53.0161483850918$$
$$x_{39} = -27.0195777004972$$
$$x_{40} = -101.016148295613$$
$$x_{41} = -55.0161483353814$$
$$x_{42} = -63.0161482971648$$
$$x_{43} = -49.0161487485998$$
$$x_{44} = -75.016148295625$$
$$x_{45} = -51.0161484969403$$
$$x_{46} = -67.0161482959196$$
$$x_{47} = -99.0161482956131$$
$$x_{48} = -105.016148295613$$
$$x_{49} = -93.0161482956131$$
Las raíces dadas
$$x_{15} = -115.016148295613$$
$$x_{20} = -113.016148295613$$
$$x_{12} = -111.016148295613$$
$$x_{7} = -109.016148295613$$
$$x_{29} = -107.016148295613$$
$$x_{48} = -105.016148295613$$
$$x_{17} = -103.016148295613$$
$$x_{40} = -101.016148295613$$
$$x_{47} = -99.0161482956131$$
$$x_{23} = -97.0161482956131$$
$$x_{32} = -95.0161482956131$$
$$x_{49} = -93.0161482956131$$
$$x_{13} = -91.0161482956131$$
$$x_{11} = -89.0161482956131$$
$$x_{37} = -87.0161482956132$$
$$x_{28} = -85.0161482956133$$
$$x_{4} = -83.0161482956135$$
$$x_{25} = -81.0161482956141$$
$$x_{8} = -79.0161482956154$$
$$x_{9} = -77.0161482956184$$
$$x_{44} = -75.016148295625$$
$$x_{22} = -73.01614829564$$
$$x_{19} = -71.0161482956736$$
$$x_{33} = -69.0161482957493$$
$$x_{46} = -67.0161482959196$$
$$x_{26} = -65.0161482963027$$
$$x_{42} = -63.0161482971648$$
$$x_{3} = -61.0161482991044$$
$$x_{21} = -59.0161483034685$$
$$x_{27} = -57.0161483132879$$
$$x_{41} = -55.0161483353814$$
$$x_{38} = -53.0161483850918$$
$$x_{45} = -51.0161484969403$$
$$x_{43} = -49.0161487485998$$
$$x_{35} = -47.0161493148352$$
$$x_{1} = -45.0161505888731$$
$$x_{14} = -43.0161534554997$$
$$x_{2} = -41.0161599056191$$
$$x_{10} = -39.0161744194484$$
$$x_{16} = -37.0162070809351$$
$$x_{36} = -35.0162805964731$$
$$x_{18} = -33.0164461441503$$
$$x_{5} = -31.0168193242027$$
$$x_{30} = -29.0176625185516$$
$$x_{39} = -27.0195777004972$$
$$x_{24} = -25.0239788561174$$
$$x_{31} = -23.0343578922278$$
$$x_{6} = -21.0602579247906$$
$$x_{34} = 0$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{15}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{15} - \frac{1}{10}$$
=
$$-115.016148295613 + - \frac{1}{10}$$
=
$$-115.116148295613$$
lo sustituimos en la expresión
$$- 2 \cdot 4^{x} + \left(6^{x} + 9^{x}\right) \leq 0$$
$$- \frac{2}{4^{115.116148295613}} + \left(9^{-115.116148295613} + 6^{-115.116148295613}\right) \leq 0$$
-9.86740039340653e-70 <= 0
significa que una de las soluciones de nuestra ecuación será con:
$$x \leq -115.016148295613$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------
x15 x20 x12 x7 x29 x48 x17 x40 x47 x23 x32 x49 x13 x11 x37 x28 x4 x25 x8 x9 x44 x22 x19 x33 x46 x26 x42 x3 x21 x27 x41 x38 x45 x43 x35 x1 x14 x2 x10 x16 x36 x18 x5 x30 x39 x24 x31 x6 x34Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \leq -115.016148295613$$
$$x \geq -113.016148295613 \wedge x \leq -111.016148295613$$
$$x \geq -109.016148295613 \wedge x \leq -107.016148295613$$
$$x \geq -105.016148295613 \wedge x \leq -103.016148295613$$
$$x \geq -101.016148295613 \wedge x \leq -99.0161482956131$$
$$x \geq -97.0161482956131 \wedge x \leq -95.0161482956131$$
$$x \geq -93.0161482956131 \wedge x \leq -91.0161482956131$$
$$x \geq -89.0161482956131 \wedge x \leq -87.0161482956132$$
$$x \geq -85.0161482956133 \wedge x \leq -83.0161482956135$$
$$x \geq -81.0161482956141 \wedge x \leq -79.0161482956154$$
$$x \geq -77.0161482956184 \wedge x \leq -75.016148295625$$
$$x \geq -73.01614829564 \wedge x \leq -71.0161482956736$$
$$x \geq -69.0161482957493 \wedge x \leq -67.0161482959196$$
$$x \geq -65.0161482963027 \wedge x \leq -63.0161482971648$$
$$x \geq -61.0161482991044 \wedge x \leq -59.0161483034685$$
$$x \geq -57.0161483132879 \wedge x \leq -55.0161483353814$$
$$x \geq -53.0161483850918 \wedge x \leq -51.0161484969403$$
$$x \geq -49.0161487485998 \wedge x \leq -47.0161493148352$$
$$x \geq -45.0161505888731 \wedge x \leq -43.0161534554997$$
$$x \geq -41.0161599056191 \wedge x \leq -39.0161744194484$$
$$x \geq -37.0162070809351 \wedge x \leq -35.0162805964731$$
$$x \geq -33.0164461441503 \wedge x \leq -31.0168193242027$$
$$x \geq -29.0176625185516 \wedge x \leq -27.0195777004972$$
$$x \geq -25.0239788561174 \wedge x \leq -23.0343578922278$$
$$x \geq -21.0602579247906 \wedge x \leq 0$$
Solución de la desigualdad en el gráfico
Gráfico