Sr Examen
Otras calculadoras
- 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:
-
4+12x>7+13x
-
x-4x^2/x-1>0
-
-x^2-2x+3>0
-
1/4x>1
-
Expresiones idénticas
- (x^ dos + seis *x+ ocho)*log(uno / cuatro , tres +sin(pi*x* uno / seis)^ dos)> uno
- (x al cuadrado más 6 multiplicar por x más 8) multiplicar por logaritmo de (1 dividir por 4,3 más seno de ( número pi multiplicar por x multiplicar por 1 dividir por 6) al cuadrado ) más 1
- (x en el grado dos más seis multiplicar por x más ocho) multiplicar por logaritmo de (uno dividir por cuatro , tres más seno de ( número pi multiplicar por x multiplicar por uno dividir por seis) en el grado dos) más uno
- (x2+6*x+8)*log(1/4,3+sin(pi*x*1/6)2)>1
- x2+6*x+8*log1/4,3+sinpi*x*1/62>1
- (x²+6*x+8)*log(1/4,3+sin(pi*x*1/6)²)>1
- (x en el grado 2+6*x+8)*log(1/4,3+sin(pi*x*1/6) en el grado 2)>1
- (x^2+6x+8)log(1/4,3+sin(pix1/6)^2)>1
- (x2+6x+8)log(1/4,3+sin(pix1/6)2)>1
- x2+6x+8log1/4,3+sinpix1/62>1
- x^2+6x+8log1/4,3+sinpix1/6^2>1
- (x^2+6*x+8)*log(1 dividir por 4,3+sin(pi*x*1 dividir por 6)^2)>1
-
Expresiones semejantes
- (x^2-6*x+8)*log(1/4,3+sin(pi*x*1/6)^2)>1
- (x^2+6*x+8)*log(1/4,3-sin(pi*x*1/6)^2)>1
- (x^2+6*x-8)*log(1/4,3+sin(pi*x*1/6)^2)>1
-
Expresiones con funciones
- Logaritmo log
- log2/3(x)-2log3(x)<=3
- log2(x^2+4x+3)>3
- log3(x+4)/(5-x)<1
- log2x<3
- log3(x)>0
- Seno sin
- sin(x)<2
- sin(pi*x)>0
- sin(x)<=1/sqrt(2)
- sin(x)<=0,5
- sin(x)<1/3
(x^2+6*x+8)*log(1/4,3+sin(pi*x*1/6)^2)>1 desigualdades
Solución
Ha introducido
[src]
/ 2 \ / 1 2/pi*x\\
\x + 6*x + 8/*log|---- + sin |----|| > 1
|/43\ \ 6 /|
||--| |
\\10/ /
$$\left(\left(x^{2} + 6 x\right) + 8\right) \log{\left(\sin^{2}{\left(\frac{\pi x}{6} \right)} + \frac{1}{\frac{43}{10}} \right)} > 1$$
(x^2 + 6*x + 8)*log(sin((pi*x)/6)^2 + 1/(43/10)) > 1
Solución detallada
Se da la desigualdad:
$$\left(\left(x^{2} + 6 x\right) + 8\right) \log{\left(\sin^{2}{\left(\frac{\pi x}{6} \right)} + \frac{1}{\frac{43}{10}} \right)} > 1$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(\left(x^{2} + 6 x\right) + 8\right) \log{\left(\sin^{2}{\left(\frac{\pi x}{6} \right)} + \frac{1}{\frac{43}{10}} \right)} = 1$$
Resolvemos:
$$x_{1} = 44.0399563314599$$
$$x_{2} = 62.0394684047451$$
$$x_{3} = 86.0392189626225$$
$$x_{4} = -87.960752990268$$
$$x_{5} = 69.9606414288391$$
$$x_{6} = 51.960317360709$$
$$x_{7} = -38.0407780688253$$
$$x_{8} = 20.0432088314978$$
$$x_{9} = -15.947398168905$$
$$x_{10} = -26.0432088314978$$
$$x_{11} = 2.13297331429678$$
$$x_{12} = -93.960792963045$$
$$x_{13} = -57.960317360709$$
$$x_{14} = -86.0392616788506$$
$$x_{15} = 57.9604576088967$$
$$x_{16} = 39.9598399598453$$
$$x_{17} = 99.9608529628847$$
$$x_{18} = -39.9594087512125$$
$$x_{19} = -81.9607035584175$$
$$x_{20} = 81.960752990268$$
$$x_{21} = -44.0402775920566$$
$$x_{22} = 80.0392616788506$$
$$x_{23} = 75.9607035584175$$
$$x_{24} = -99.9608257449484$$
$$x_{25} = -33.9587022825868$$
$$x_{26} = -50.0399563314599$$
$$x_{27} = -74.0393818699341$$
$$x_{28} = -45.9598399598453$$
$$x_{29} = 26.0416209775957$$
$$x_{30} = -68.0394684047451$$
$$x_{31} = -32.0416209775957$$
$$x_{32} = -75.9606414288391$$
$$x_{33} = 50.0397378990539$$
$$x_{34} = 3.91137210005719$$
$$x_{35} = -51.9601223774976$$
$$x_{36} = -98.0391840809125$$
$$x_{37} = 14.0467731248464$$
$$x_{38} = 92.0391840809125$$
$$x_{39} = 27.9587022825868$$
$$x_{40} = 56.0395826650111$$
$$x_{41} = 33.9594087512125$$
$$x_{42} = 32.0407780688253$$
$$x_{43} = 63.9605618478227$$
$$x_{44} = -92.0392189626225$$
$$x_{45} = 98.0391552285943$$
$$x_{46} = -27.957424098254$$
$$x_{47} = -80.0393147646128$$
$$x_{48} = 38.0402775920566$$
$$x_{49} = -14.0577682683149$$
$$x_{50} = 74.0393147646128$$
$$x_{51} = 68.0393818699341$$
$$x_{52} = -69.9605618478227$$
$$x_{53} = 87.960792963045$$
$$x_{54} = -9.91137210005719$$
$$x_{55} = -62.0395826650111$$
$$x_{56} = 8.0577682683149$$
$$x_{57} = -21.954735126445$$
$$x_{58} = 45.9601223774976$$
$$x_{59} = 15.954735126445$$
$$x_{60} = -8.13297331429678$$
$$x_{61} = 93.9608257449484$$
$$x_{62} = -56.0397378990539$$
$$x_{63} = 9.94739816890502$$
$$x_{64} = -20.0467731248464$$
$$x_{65} = -63.9604576088967$$
$$x_{66} = 21.957424098254$$
$$x_{1} = 44.0399563314599$$
$$x_{2} = 62.0394684047451$$
$$x_{3} = 86.0392189626225$$
$$x_{4} = -87.960752990268$$
$$x_{5} = 69.9606414288391$$
$$x_{6} = 51.960317360709$$
$$x_{7} = -38.0407780688253$$
$$x_{8} = 20.0432088314978$$
$$x_{9} = -15.947398168905$$
$$x_{10} = -26.0432088314978$$
$$x_{11} = 2.13297331429678$$
$$x_{12} = -93.960792963045$$
$$x_{13} = -57.960317360709$$
$$x_{14} = -86.0392616788506$$
$$x_{15} = 57.9604576088967$$
$$x_{16} = 39.9598399598453$$
$$x_{17} = 99.9608529628847$$
$$x_{18} = -39.9594087512125$$
$$x_{19} = -81.9607035584175$$
$$x_{20} = 81.960752990268$$
$$x_{21} = -44.0402775920566$$
$$x_{22} = 80.0392616788506$$
$$x_{23} = 75.9607035584175$$
$$x_{24} = -99.9608257449484$$
$$x_{25} = -33.9587022825868$$
$$x_{26} = -50.0399563314599$$
$$x_{27} = -74.0393818699341$$
$$x_{28} = -45.9598399598453$$
$$x_{29} = 26.0416209775957$$
$$x_{30} = -68.0394684047451$$
$$x_{31} = -32.0416209775957$$
$$x_{32} = -75.9606414288391$$
$$x_{33} = 50.0397378990539$$
$$x_{34} = 3.91137210005719$$
$$x_{35} = -51.9601223774976$$
$$x_{36} = -98.0391840809125$$
$$x_{37} = 14.0467731248464$$
$$x_{38} = 92.0391840809125$$
$$x_{39} = 27.9587022825868$$
$$x_{40} = 56.0395826650111$$
$$x_{41} = 33.9594087512125$$
$$x_{42} = 32.0407780688253$$
$$x_{43} = 63.9605618478227$$
$$x_{44} = -92.0392189626225$$
$$x_{45} = 98.0391552285943$$
$$x_{46} = -27.957424098254$$
$$x_{47} = -80.0393147646128$$
$$x_{48} = 38.0402775920566$$
$$x_{49} = -14.0577682683149$$
$$x_{50} = 74.0393147646128$$
$$x_{51} = 68.0393818699341$$
$$x_{52} = -69.9605618478227$$
$$x_{53} = 87.960792963045$$
$$x_{54} = -9.91137210005719$$
$$x_{55} = -62.0395826650111$$
$$x_{56} = 8.0577682683149$$
$$x_{57} = -21.954735126445$$
$$x_{58} = 45.9601223774976$$
$$x_{59} = 15.954735126445$$
$$x_{60} = -8.13297331429678$$
$$x_{61} = 93.9608257449484$$
$$x_{62} = -56.0397378990539$$
$$x_{63} = 9.94739816890502$$
$$x_{64} = -20.0467731248464$$
$$x_{65} = -63.9604576088967$$
$$x_{66} = 21.957424098254$$
Las raíces dadas
$$x_{24} = -99.9608257449484$$
$$x_{36} = -98.0391840809125$$
$$x_{12} = -93.960792963045$$
$$x_{44} = -92.0392189626225$$
$$x_{4} = -87.960752990268$$
$$x_{14} = -86.0392616788506$$
$$x_{19} = -81.9607035584175$$
$$x_{47} = -80.0393147646128$$
$$x_{32} = -75.9606414288391$$
$$x_{27} = -74.0393818699341$$
$$x_{52} = -69.9605618478227$$
$$x_{30} = -68.0394684047451$$
$$x_{65} = -63.9604576088967$$
$$x_{55} = -62.0395826650111$$
$$x_{13} = -57.960317360709$$
$$x_{62} = -56.0397378990539$$
$$x_{35} = -51.9601223774976$$
$$x_{26} = -50.0399563314599$$
$$x_{28} = -45.9598399598453$$
$$x_{21} = -44.0402775920566$$
$$x_{18} = -39.9594087512125$$
$$x_{7} = -38.0407780688253$$
$$x_{25} = -33.9587022825868$$
$$x_{31} = -32.0416209775957$$
$$x_{46} = -27.957424098254$$
$$x_{10} = -26.0432088314978$$
$$x_{57} = -21.954735126445$$
$$x_{64} = -20.0467731248464$$
$$x_{9} = -15.947398168905$$
$$x_{49} = -14.0577682683149$$
$$x_{54} = -9.91137210005719$$
$$x_{60} = -8.13297331429678$$
$$x_{11} = 2.13297331429678$$
$$x_{34} = 3.91137210005719$$
$$x_{56} = 8.0577682683149$$
$$x_{63} = 9.94739816890502$$
$$x_{37} = 14.0467731248464$$
$$x_{59} = 15.954735126445$$
$$x_{8} = 20.0432088314978$$
$$x_{66} = 21.957424098254$$
$$x_{29} = 26.0416209775957$$
$$x_{39} = 27.9587022825868$$
$$x_{42} = 32.0407780688253$$
$$x_{41} = 33.9594087512125$$
$$x_{48} = 38.0402775920566$$
$$x_{16} = 39.9598399598453$$
$$x_{1} = 44.0399563314599$$
$$x_{58} = 45.9601223774976$$
$$x_{33} = 50.0397378990539$$
$$x_{6} = 51.960317360709$$
$$x_{40} = 56.0395826650111$$
$$x_{15} = 57.9604576088967$$
$$x_{2} = 62.0394684047451$$
$$x_{43} = 63.9605618478227$$
$$x_{51} = 68.0393818699341$$
$$x_{5} = 69.9606414288391$$
$$x_{50} = 74.0393147646128$$
$$x_{23} = 75.9607035584175$$
$$x_{22} = 80.0392616788506$$
$$x_{20} = 81.960752990268$$
$$x_{3} = 86.0392189626225$$
$$x_{53} = 87.960792963045$$
$$x_{38} = 92.0391840809125$$
$$x_{61} = 93.9608257449484$$
$$x_{45} = 98.0391552285943$$
$$x_{17} = 99.9608529628847$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{24}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{24} - \frac{1}{10}$$
=
$$-99.9608257449484 + - \frac{1}{10}$$
=
$$-100.060825744948$$
lo sustituimos en la expresión
$$\left(\left(x^{2} + 6 x\right) + 8\right) \log{\left(\sin^{2}{\left(\frac{\pi x}{6} \right)} + \frac{1}{\frac{43}{10}} \right)} > 1$$
$$\left(8 + \left(\left(-100.060825744948\right) 6 + \left(-100.060825744948\right)^{2}\right)\right) \log{\left(\frac{1}{\frac{43}{10}} + \sin^{2}{\left(\frac{\left(-100.060825744948\right) \pi}{6} \right)} \right)} > 1$$
Entonces
$$x < -99.9608257449484$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -99.9608257449484 \wedge x < -98.0391840809125$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -99.9608257449484 \wedge x < -98.0391840809125$$
$$x > -93.960792963045 \wedge x < -92.0392189626225$$
$$x > -87.960752990268 \wedge x < -86.0392616788506$$
$$x > -81.9607035584175 \wedge x < -80.0393147646128$$
$$x > -75.9606414288391 \wedge x < -74.0393818699341$$
$$x > -69.9605618478227 \wedge x < -68.0394684047451$$
$$x > -63.9604576088967 \wedge x < -62.0395826650111$$
$$x > -57.960317360709 \wedge x < -56.0397378990539$$
$$x > -51.9601223774976 \wedge x < -50.0399563314599$$
$$x > -45.9598399598453 \wedge x < -44.0402775920566$$
$$x > -39.9594087512125 \wedge x < -38.0407780688253$$
$$x > -33.9587022825868 \wedge x < -32.0416209775957$$
$$x > -27.957424098254 \wedge x < -26.0432088314978$$
$$x > -21.954735126445 \wedge x < -20.0467731248464$$
$$x > -15.947398168905 \wedge x < -14.0577682683149$$
$$x > -9.91137210005719 \wedge x < -8.13297331429678$$
$$x > 2.13297331429678 \wedge x < 3.91137210005719$$
$$x > 8.0577682683149 \wedge x < 9.94739816890502$$
$$x > 14.0467731248464 \wedge x < 15.954735126445$$
$$x > 20.0432088314978 \wedge x < 21.957424098254$$
$$x > 26.0416209775957 \wedge x < 27.9587022825868$$
$$x > 32.0407780688253 \wedge x < 33.9594087512125$$
$$x > 38.0402775920566 \wedge x < 39.9598399598453$$
$$x > 44.0399563314599 \wedge x < 45.9601223774976$$
$$x > 50.0397378990539 \wedge x < 51.960317360709$$
$$x > 56.0395826650111 \wedge x < 57.9604576088967$$
$$x > 62.0394684047451 \wedge x < 63.9605618478227$$
$$x > 68.0393818699341 \wedge x < 69.9606414288391$$
$$x > 74.0393147646128 \wedge x < 75.9607035584175$$
$$x > 80.0392616788506 \wedge x < 81.960752990268$$
$$x > 86.0392189626225 \wedge x < 87.960792963045$$
$$x > 92.0391840809125 \wedge x < 93.9608257449484$$
$$x > 98.0391552285943 \wedge x < 99.9608529628847$$
$$\left(\left(x^{2} + 6 x\right) + 8\right) \log{\left(\sin^{2}{\left(\frac{\pi x}{6} \right)} + \frac{1}{\frac{43}{10}} \right)} > 1$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(\left(x^{2} + 6 x\right) + 8\right) \log{\left(\sin^{2}{\left(\frac{\pi x}{6} \right)} + \frac{1}{\frac{43}{10}} \right)} = 1$$
Resolvemos:
$$x_{1} = 44.0399563314599$$
$$x_{2} = 62.0394684047451$$
$$x_{3} = 86.0392189626225$$
$$x_{4} = -87.960752990268$$
$$x_{5} = 69.9606414288391$$
$$x_{6} = 51.960317360709$$
$$x_{7} = -38.0407780688253$$
$$x_{8} = 20.0432088314978$$
$$x_{9} = -15.947398168905$$
$$x_{10} = -26.0432088314978$$
$$x_{11} = 2.13297331429678$$
$$x_{12} = -93.960792963045$$
$$x_{13} = -57.960317360709$$
$$x_{14} = -86.0392616788506$$
$$x_{15} = 57.9604576088967$$
$$x_{16} = 39.9598399598453$$
$$x_{17} = 99.9608529628847$$
$$x_{18} = -39.9594087512125$$
$$x_{19} = -81.9607035584175$$
$$x_{20} = 81.960752990268$$
$$x_{21} = -44.0402775920566$$
$$x_{22} = 80.0392616788506$$
$$x_{23} = 75.9607035584175$$
$$x_{24} = -99.9608257449484$$
$$x_{25} = -33.9587022825868$$
$$x_{26} = -50.0399563314599$$
$$x_{27} = -74.0393818699341$$
$$x_{28} = -45.9598399598453$$
$$x_{29} = 26.0416209775957$$
$$x_{30} = -68.0394684047451$$
$$x_{31} = -32.0416209775957$$
$$x_{32} = -75.9606414288391$$
$$x_{33} = 50.0397378990539$$
$$x_{34} = 3.91137210005719$$
$$x_{35} = -51.9601223774976$$
$$x_{36} = -98.0391840809125$$
$$x_{37} = 14.0467731248464$$
$$x_{38} = 92.0391840809125$$
$$x_{39} = 27.9587022825868$$
$$x_{40} = 56.0395826650111$$
$$x_{41} = 33.9594087512125$$
$$x_{42} = 32.0407780688253$$
$$x_{43} = 63.9605618478227$$
$$x_{44} = -92.0392189626225$$
$$x_{45} = 98.0391552285943$$
$$x_{46} = -27.957424098254$$
$$x_{47} = -80.0393147646128$$
$$x_{48} = 38.0402775920566$$
$$x_{49} = -14.0577682683149$$
$$x_{50} = 74.0393147646128$$
$$x_{51} = 68.0393818699341$$
$$x_{52} = -69.9605618478227$$
$$x_{53} = 87.960792963045$$
$$x_{54} = -9.91137210005719$$
$$x_{55} = -62.0395826650111$$
$$x_{56} = 8.0577682683149$$
$$x_{57} = -21.954735126445$$
$$x_{58} = 45.9601223774976$$
$$x_{59} = 15.954735126445$$
$$x_{60} = -8.13297331429678$$
$$x_{61} = 93.9608257449484$$
$$x_{62} = -56.0397378990539$$
$$x_{63} = 9.94739816890502$$
$$x_{64} = -20.0467731248464$$
$$x_{65} = -63.9604576088967$$
$$x_{66} = 21.957424098254$$
$$x_{1} = 44.0399563314599$$
$$x_{2} = 62.0394684047451$$
$$x_{3} = 86.0392189626225$$
$$x_{4} = -87.960752990268$$
$$x_{5} = 69.9606414288391$$
$$x_{6} = 51.960317360709$$
$$x_{7} = -38.0407780688253$$
$$x_{8} = 20.0432088314978$$
$$x_{9} = -15.947398168905$$
$$x_{10} = -26.0432088314978$$
$$x_{11} = 2.13297331429678$$
$$x_{12} = -93.960792963045$$
$$x_{13} = -57.960317360709$$
$$x_{14} = -86.0392616788506$$
$$x_{15} = 57.9604576088967$$
$$x_{16} = 39.9598399598453$$
$$x_{17} = 99.9608529628847$$
$$x_{18} = -39.9594087512125$$
$$x_{19} = -81.9607035584175$$
$$x_{20} = 81.960752990268$$
$$x_{21} = -44.0402775920566$$
$$x_{22} = 80.0392616788506$$
$$x_{23} = 75.9607035584175$$
$$x_{24} = -99.9608257449484$$
$$x_{25} = -33.9587022825868$$
$$x_{26} = -50.0399563314599$$
$$x_{27} = -74.0393818699341$$
$$x_{28} = -45.9598399598453$$
$$x_{29} = 26.0416209775957$$
$$x_{30} = -68.0394684047451$$
$$x_{31} = -32.0416209775957$$
$$x_{32} = -75.9606414288391$$
$$x_{33} = 50.0397378990539$$
$$x_{34} = 3.91137210005719$$
$$x_{35} = -51.9601223774976$$
$$x_{36} = -98.0391840809125$$
$$x_{37} = 14.0467731248464$$
$$x_{38} = 92.0391840809125$$
$$x_{39} = 27.9587022825868$$
$$x_{40} = 56.0395826650111$$
$$x_{41} = 33.9594087512125$$
$$x_{42} = 32.0407780688253$$
$$x_{43} = 63.9605618478227$$
$$x_{44} = -92.0392189626225$$
$$x_{45} = 98.0391552285943$$
$$x_{46} = -27.957424098254$$
$$x_{47} = -80.0393147646128$$
$$x_{48} = 38.0402775920566$$
$$x_{49} = -14.0577682683149$$
$$x_{50} = 74.0393147646128$$
$$x_{51} = 68.0393818699341$$
$$x_{52} = -69.9605618478227$$
$$x_{53} = 87.960792963045$$
$$x_{54} = -9.91137210005719$$
$$x_{55} = -62.0395826650111$$
$$x_{56} = 8.0577682683149$$
$$x_{57} = -21.954735126445$$
$$x_{58} = 45.9601223774976$$
$$x_{59} = 15.954735126445$$
$$x_{60} = -8.13297331429678$$
$$x_{61} = 93.9608257449484$$
$$x_{62} = -56.0397378990539$$
$$x_{63} = 9.94739816890502$$
$$x_{64} = -20.0467731248464$$
$$x_{65} = -63.9604576088967$$
$$x_{66} = 21.957424098254$$
Las raíces dadas
$$x_{24} = -99.9608257449484$$
$$x_{36} = -98.0391840809125$$
$$x_{12} = -93.960792963045$$
$$x_{44} = -92.0392189626225$$
$$x_{4} = -87.960752990268$$
$$x_{14} = -86.0392616788506$$
$$x_{19} = -81.9607035584175$$
$$x_{47} = -80.0393147646128$$
$$x_{32} = -75.9606414288391$$
$$x_{27} = -74.0393818699341$$
$$x_{52} = -69.9605618478227$$
$$x_{30} = -68.0394684047451$$
$$x_{65} = -63.9604576088967$$
$$x_{55} = -62.0395826650111$$
$$x_{13} = -57.960317360709$$
$$x_{62} = -56.0397378990539$$
$$x_{35} = -51.9601223774976$$
$$x_{26} = -50.0399563314599$$
$$x_{28} = -45.9598399598453$$
$$x_{21} = -44.0402775920566$$
$$x_{18} = -39.9594087512125$$
$$x_{7} = -38.0407780688253$$
$$x_{25} = -33.9587022825868$$
$$x_{31} = -32.0416209775957$$
$$x_{46} = -27.957424098254$$
$$x_{10} = -26.0432088314978$$
$$x_{57} = -21.954735126445$$
$$x_{64} = -20.0467731248464$$
$$x_{9} = -15.947398168905$$
$$x_{49} = -14.0577682683149$$
$$x_{54} = -9.91137210005719$$
$$x_{60} = -8.13297331429678$$
$$x_{11} = 2.13297331429678$$
$$x_{34} = 3.91137210005719$$
$$x_{56} = 8.0577682683149$$
$$x_{63} = 9.94739816890502$$
$$x_{37} = 14.0467731248464$$
$$x_{59} = 15.954735126445$$
$$x_{8} = 20.0432088314978$$
$$x_{66} = 21.957424098254$$
$$x_{29} = 26.0416209775957$$
$$x_{39} = 27.9587022825868$$
$$x_{42} = 32.0407780688253$$
$$x_{41} = 33.9594087512125$$
$$x_{48} = 38.0402775920566$$
$$x_{16} = 39.9598399598453$$
$$x_{1} = 44.0399563314599$$
$$x_{58} = 45.9601223774976$$
$$x_{33} = 50.0397378990539$$
$$x_{6} = 51.960317360709$$
$$x_{40} = 56.0395826650111$$
$$x_{15} = 57.9604576088967$$
$$x_{2} = 62.0394684047451$$
$$x_{43} = 63.9605618478227$$
$$x_{51} = 68.0393818699341$$
$$x_{5} = 69.9606414288391$$
$$x_{50} = 74.0393147646128$$
$$x_{23} = 75.9607035584175$$
$$x_{22} = 80.0392616788506$$
$$x_{20} = 81.960752990268$$
$$x_{3} = 86.0392189626225$$
$$x_{53} = 87.960792963045$$
$$x_{38} = 92.0391840809125$$
$$x_{61} = 93.9608257449484$$
$$x_{45} = 98.0391552285943$$
$$x_{17} = 99.9608529628847$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{24}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{24} - \frac{1}{10}$$
=
$$-99.9608257449484 + - \frac{1}{10}$$
=
$$-100.060825744948$$
lo sustituimos en la expresión
$$\left(\left(x^{2} + 6 x\right) + 8\right) \log{\left(\sin^{2}{\left(\frac{\pi x}{6} \right)} + \frac{1}{\frac{43}{10}} \right)} > 1$$
$$\left(8 + \left(\left(-100.060825744948\right) 6 + \left(-100.060825744948\right)^{2}\right)\right) \log{\left(\frac{1}{\frac{43}{10}} + \sin^{2}{\left(\frac{\left(-100.060825744948\right) \pi}{6} \right)} \right)} > 1$$
/10 2 \
9419.80389429124*log|-- + sin (0.676804290824734*pi)| > 1
\43 / Entonces
$$x < -99.9608257449484$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -99.9608257449484 \wedge x < -98.0391840809125$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------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-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
x24 x36 x12 x44 x4 x14 x19 x47 x32 x27 x52 x30 x65 x55 x13 x62 x35 x26 x28 x21 x18 x7 x25 x31 x46 x10 x57 x64 x9 x49 x54 x60 x11 x34 x56 x63 x37 x59 x8 x66 x29 x39 x42 x41 x48 x16 x1 x58 x33 x6 x40 x15 x2 x43 x51 x5 x50 x23 x22 x20 x3 x53 x38 x61 x45 x17Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -99.9608257449484 \wedge x < -98.0391840809125$$
$$x > -93.960792963045 \wedge x < -92.0392189626225$$
$$x > -87.960752990268 \wedge x < -86.0392616788506$$
$$x > -81.9607035584175 \wedge x < -80.0393147646128$$
$$x > -75.9606414288391 \wedge x < -74.0393818699341$$
$$x > -69.9605618478227 \wedge x < -68.0394684047451$$
$$x > -63.9604576088967 \wedge x < -62.0395826650111$$
$$x > -57.960317360709 \wedge x < -56.0397378990539$$
$$x > -51.9601223774976 \wedge x < -50.0399563314599$$
$$x > -45.9598399598453 \wedge x < -44.0402775920566$$
$$x > -39.9594087512125 \wedge x < -38.0407780688253$$
$$x > -33.9587022825868 \wedge x < -32.0416209775957$$
$$x > -27.957424098254 \wedge x < -26.0432088314978$$
$$x > -21.954735126445 \wedge x < -20.0467731248464$$
$$x > -15.947398168905 \wedge x < -14.0577682683149$$
$$x > -9.91137210005719 \wedge x < -8.13297331429678$$
$$x > 2.13297331429678 \wedge x < 3.91137210005719$$
$$x > 8.0577682683149 \wedge x < 9.94739816890502$$
$$x > 14.0467731248464 \wedge x < 15.954735126445$$
$$x > 20.0432088314978 \wedge x < 21.957424098254$$
$$x > 26.0416209775957 \wedge x < 27.9587022825868$$
$$x > 32.0407780688253 \wedge x < 33.9594087512125$$
$$x > 38.0402775920566 \wedge x < 39.9598399598453$$
$$x > 44.0399563314599 \wedge x < 45.9601223774976$$
$$x > 50.0397378990539 \wedge x < 51.960317360709$$
$$x > 56.0395826650111 \wedge x < 57.9604576088967$$
$$x > 62.0394684047451 \wedge x < 63.9605618478227$$
$$x > 68.0393818699341 \wedge x < 69.9606414288391$$
$$x > 74.0393147646128 \wedge x < 75.9607035584175$$
$$x > 80.0392616788506 \wedge x < 81.960752990268$$
$$x > 86.0392189626225 \wedge x < 87.960792963045$$
$$x > 92.0391840809125 \wedge x < 93.9608257449484$$
$$x > 98.0391552285943 \wedge x < 99.9608529628847$$
Solución de la desigualdad en el gráfico