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:
- (x-a)(2x-1)(x+b)>0
-
(x-6)*(x+1)>0
-
6x^2+x-1>0
-
x^2<=0
-
Expresiones idénticas
- (x- tres)(x- uno)log[cos(pix)^ dos +cosx+ dos sin(x/ dos)^ dos , dos ^(uno / dos)/ dos ]>=2
- (x menos 3)(x menos 1) logaritmo de [ coseno de ( número pi x) al cuadrado más coseno de x más 2 seno de (x dividir por 2) al cuadrado ,2 en el grado (1 dividir por 2) dividir por 2] más o igual a 2
- (x menos tres)(x menos uno) logaritmo de [ coseno de ( número pi x) en el grado dos más coseno de x más dos seno de (x dividir por dos) en el grado dos , dos en el grado (uno dividir por dos) dividir por dos ] más o igual a 2
- (x-3)(x-1)log[cos(pix)2+cosx+2sin(x/2)2,2(1/2)/2]>=2
- x-3x-1log[cospix2+cosx+2sinx/22,21/2/2]>=2
- (x-3)(x-1)log[cos(pix)²+cosx+2sin(x/2)²,2^(1/2)/2]>=2
- (x-3)(x-1)log[cos(pix) en el grado 2+cosx+2sin(x/2) en el grado 2,2 en el grado (1/2)/2]>=2
- x-3x-1log[cospix^2+cosx+2sinx/2^2,2^1/2/2]>=2
- (x-3)(x-1)log[cos(pix)^2+cosx+2sin(x dividir por 2)^2,2^(1 dividir por 2) dividir por 2]>=2
-
Expresiones semejantes
- (x+3)(x-1)log[cos(pix)^2+cosx+2sin(x/2)^2,2^(1/2)/2]>=2
- (x-3)(x+1)log[cos(pix)^2+cosx+2sin(x/2)^2,2^(1/2)/2]>=2
- (x-3)(x-1)log[cos(pix)^2+cosx-2sin(x/2)^2,2^(1/2)/2]>=2
- (x-3)(x-1)log[cos(pix)^2-cosx+2sin(x/2)^2,2^(1/2)/2]>=2
-
Expresiones con funciones
- Logaritmo log
- log(x)^2>0
- log_9(2x+3)<0
- log9(2x+3)<0
- log9x<-1
- loga(5-x)>=loga(4x-35)
- Coseno cos
- cos2x<0,5
- cos(x-pi/4)<1/(sqrt(2))
- cos<=-(√2/2)
- cos(x)>_√3
- cos(2пx)>0
(x-3)(x-1)log[cos(pix)^2+cosx+2sin(x/2)^2,2^(1/2)/2]>=2 desigualdades
Solución
Ha introducido
[src]
/ ______\
| \/ 11/5 |
| / /x\\ |
| 2*|sin|-|| |
| 2 \ \2// |
(x - 3)*(x - 1)*log|cos (pi*x) + cos(x) + ------------------| >= 2
\ 2 /
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\left(\cos{\left(x \right)} + \cos^{2}{\left(\pi x \right)}\right) + \frac{2 \sin^{\sqrt{\frac{11}{5}}}{\left(\frac{x}{2} \right)}}{2} \right)} \geq 2$$
((x - 3)*(x - 1))*log(cos(x) + cos(pi*x)^2 + (2*sin(x/2)^(sqrt(11/5)))/2) >= 2
Solución detallada
Se da la desigualdad:
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\left(\cos{\left(x \right)} + \cos^{2}{\left(\pi x \right)}\right) + \frac{2 \sin^{\sqrt{\frac{11}{5}}}{\left(\frac{x}{2} \right)}}{2} \right)} \geq 2$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\left(\cos{\left(x \right)} + \cos^{2}{\left(\pi x \right)}\right) + \frac{2 \sin^{\sqrt{\frac{11}{5}}}{\left(\frac{x}{2} \right)}}{2} \right)} = 2$$
Resolvemos:
$$x_{1} = 100.510435418134 - 0.0047674147312816 i$$
$$x_{2} = 68.5297227402575$$
$$x_{3} = -93.6529547362519 - 0.0504357558232563 i$$
$$x_{4} = 52.2132777167091$$
$$x_{5} = 94.4430446648741 + 0.0239734809090849 i$$
$$x_{6} = 40.1269090033684$$
$$x_{7} = -33.8796199609159$$
$$x_{8} = 8.08522178928987 + 0.221804327440013 i$$
$$x_{9} = 42.2523150363882$$
$$x_{10} = -87.4951623536677 + 0.0264918224471817 i$$
$$x_{11} = -61.6484065733173$$
$$x_{12} = -67.8271064885251 - 0.116532580524128 i$$
$$x_{13} = -41.919402019937 + 0.253793657662776 i$$
$$x_{14} = -83.8209630426373$$
$$x_{15} = -47.8674926836918$$
$$x_{16} = 90.1676573854581$$
$$x_{17} = -16.9160112621997 + 0.236091194526466 i$$
$$x_{18} = -7.69765946779217$$
$$x_{19} = 0.0259969878312562$$
$$x_{20} = 58.1159652901164 - 0.168943046399089 i$$
$$x_{21} = 28.0383674979943$$
$$x_{22} = 44.3912217448768 - 0.0386843113446253 i$$
$$x_{23} = 14.2557271704627$$
$$x_{24} = -57.6296158327081$$
$$x_{25} = -95.3640346092024$$
$$x_{26} = -95.6965840882506$$
$$x_{27} = 73.8767048669985 + 0.159634370423093 i$$
$$x_{28} = 56.5037427905596 + 0.0142885202923343 i$$
$$x_{29} = -5.66932787023074 - 0.0497064137401943 i$$
$$x_{30} = 88.519795836584$$
$$x_{31} = 26.3451765828346$$
$$x_{32} = -71.9446304817941$$
$$x_{33} = 92.1945249026872$$
$$x_{34} = 54.128574941131$$
$$x_{35} = -81.5428971975277 - 0.0191245612540122 i$$
$$x_{36} = 15.9671278777495$$
$$x_{37} = 80.3190541652628$$
$$x_{38} = -73.7353154660035$$
$$x_{39} = 64.2998397574696$$
$$x_{40} = 35.9079872393627 - 0.212205057974673 i$$
$$x_{41} = -52.089956603758 - 0.217871757172483 i$$
$$x_{42} = 32.2802458587386 - 0.0691505085823875 i$$
$$x_{43} = -66.9212508083606 + 0.269489880500199 i$$
$$x_{44} = 20.164782218209 - 0.121405581267706 i$$
$$x_{45} = 92.7122815315705$$
$$x_{46} = -99.6012951400255$$
$$x_{47} = 6.38590519069954 - 0.00575895418760668 i$$
$$x_{48} = -54.8953300391768 - 0.186195356732807 i$$
$$x_{49} = -31.4961106304242 - 0.0191707060545047 i$$
$$x_{50} = -14.1170844576311 - 0.166541967937758 i$$
$$x_{51} = -23.6954544888424$$
$$x_{52} = 82.3332156159097 - 0.0540938198971391 i$$
$$x_{53} = -29.8795040594379 - 0.162851569333039 i$$
$$x_{54} = -2.07254282841937 - 0.270802694872933 i$$
$$x_{55} = -17.7742905308476 - 0.0886248084834091 i$$
$$x_{56} = -19.4587884353761$$
$$x_{57} = -59.9535607517084$$
$$x_{58} = -45.7553208896104$$
$$x_{59} = 111.823557484907 + 0.114305309917005 i$$
$$x_{60} = 50.4985071395553 - 0.0369607780358167 i$$
$$x_{61} = 76.3874647847242$$
$$x_{62} = -35.7814970140969$$
$$x_{63} = 11.7207671633765 - 0.0672315020436625 i$$
$$x_{64} = -49.4130262826674$$
$$x_{65} = -75.4734559804639 - 0.0125866265148061 i$$
$$x_{66} = 3.28658644133219 - 0.369342697073948 i$$
$$x_{67} = 38.5957978455979$$
$$x_{68} = 5.30170266613166$$
$$x_{69} = -9.92049181202345$$
$$x_{70} = 85.9189522586373 - 0.251433509912749 i$$
$$x_{71} = -25.4194772379531 - 0.0303405831403926 i$$
$$x_{72} = -55.7122976199228 - 0.0670079176742718 i$$
$$x_{73} = -37.5022710508658 + 0.0343942270405407 i$$
$$x_{74} = 18.4984592764267 - 0.0265263451148552 i$$
$$x_{75} = -43.6019102829849 - 0.0368709510682677 i$$
$$x_{76} = -11.6114441043886$$
$$x_{77} = -97.9075682228443$$
$$x_{78} = 70.2194936875721 - 0.0917905796213954 i$$
$$x_{79} = -80.7389286380715 + 0.075669195211865 i$$
$$x_{80} = -40.9095455028656 - 0.321103912982183 i$$
$$x_{81} = -85.8215792771042$$
$$x_{82} = 62.5726892695298 - 0.0287324695214719 i$$
$$x_{83} = 12.543766196288 - 0.00146153110638568 i$$
$$x_{84} = 78.081604889231$$
Descartamos las soluciones complejas:
$$x_{1} = 68.5297227402575$$
$$x_{2} = 52.2132777167091$$
$$x_{3} = 40.1269090033684$$
$$x_{4} = -33.8796199609159$$
$$x_{5} = 42.2523150363882$$
$$x_{6} = -61.6484065733173$$
$$x_{7} = -83.8209630426373$$
$$x_{8} = -47.8674926836918$$
$$x_{9} = 90.1676573854581$$
$$x_{10} = -7.69765946779217$$
$$x_{11} = 0.0259969878312562$$
$$x_{12} = 28.0383674979943$$
$$x_{13} = 14.2557271704627$$
$$x_{14} = -57.6296158327081$$
$$x_{15} = -95.3640346092024$$
$$x_{16} = -95.6965840882506$$
$$x_{17} = 88.519795836584$$
$$x_{18} = 26.3451765828346$$
$$x_{19} = -71.9446304817941$$
$$x_{20} = 92.1945249026872$$
$$x_{21} = 54.128574941131$$
$$x_{22} = 15.9671278777495$$
$$x_{23} = 80.3190541652628$$
$$x_{24} = -73.7353154660035$$
$$x_{25} = 64.2998397574696$$
$$x_{26} = 92.7122815315705$$
$$x_{27} = -99.6012951400255$$
$$x_{28} = -23.6954544888424$$
$$x_{29} = -19.4587884353761$$
$$x_{30} = -59.9535607517084$$
$$x_{31} = -45.7553208896104$$
$$x_{32} = 76.3874647847242$$
$$x_{33} = -35.7814970140969$$
$$x_{34} = -49.4130262826674$$
$$x_{35} = 38.5957978455979$$
$$x_{36} = 5.30170266613166$$
$$x_{37} = -9.92049181202345$$
$$x_{38} = -11.6114441043886$$
$$x_{39} = -97.9075682228443$$
$$x_{40} = -85.8215792771042$$
$$x_{41} = 78.081604889231$$
Las raíces dadas
$$x_{27} = -99.6012951400255$$
$$x_{39} = -97.9075682228443$$
$$x_{16} = -95.6965840882506$$
$$x_{15} = -95.3640346092024$$
$$x_{40} = -85.8215792771042$$
$$x_{7} = -83.8209630426373$$
$$x_{24} = -73.7353154660035$$
$$x_{19} = -71.9446304817941$$
$$x_{6} = -61.6484065733173$$
$$x_{30} = -59.9535607517084$$
$$x_{14} = -57.6296158327081$$
$$x_{34} = -49.4130262826674$$
$$x_{8} = -47.8674926836918$$
$$x_{31} = -45.7553208896104$$
$$x_{33} = -35.7814970140969$$
$$x_{4} = -33.8796199609159$$
$$x_{28} = -23.6954544888424$$
$$x_{29} = -19.4587884353761$$
$$x_{38} = -11.6114441043886$$
$$x_{37} = -9.92049181202345$$
$$x_{10} = -7.69765946779217$$
$$x_{11} = 0.0259969878312562$$
$$x_{36} = 5.30170266613166$$
$$x_{13} = 14.2557271704627$$
$$x_{22} = 15.9671278777495$$
$$x_{18} = 26.3451765828346$$
$$x_{12} = 28.0383674979943$$
$$x_{35} = 38.5957978455979$$
$$x_{3} = 40.1269090033684$$
$$x_{5} = 42.2523150363882$$
$$x_{2} = 52.2132777167091$$
$$x_{21} = 54.128574941131$$
$$x_{25} = 64.2998397574696$$
$$x_{1} = 68.5297227402575$$
$$x_{32} = 76.3874647847242$$
$$x_{41} = 78.081604889231$$
$$x_{23} = 80.3190541652628$$
$$x_{17} = 88.519795836584$$
$$x_{9} = 90.1676573854581$$
$$x_{20} = 92.1945249026872$$
$$x_{26} = 92.7122815315705$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{27}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{27} - \frac{1}{10}$$
=
$$-99.6012951400255 + - \frac{1}{10}$$
=
$$-99.7012951400255$$
lo sustituimos en la expresión
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\left(\cos{\left(x \right)} + \cos^{2}{\left(\pi x \right)}\right) + \frac{2 \sin^{\sqrt{\frac{11}{5}}}{\left(\frac{x}{2} \right)}}{2} \right)} \geq 2$$
$$\left(-99.7012951400255 - 3\right) \left(-99.7012951400255 - 1\right) \log{\left(\frac{2 \sin^{\sqrt{\frac{11}{5}}}{\left(- \frac{99.7012951400255}{2} \right)}}{2} + \left(\cos^{2}{\left(\left(-99.7012951400255\right) \pi \right)} + \cos{\left(-99.7012951400255 \right)}\right) \right)} \geq 2$$
significa que una de las soluciones de nuestra ecuación será con:
$$x \leq -99.6012951400255$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \leq -99.6012951400255$$
$$x \geq -97.9075682228443 \wedge x \leq -95.6965840882506$$
$$x \geq -95.3640346092024 \wedge x \leq -85.8215792771042$$
$$x \geq -83.8209630426373 \wedge x \leq -73.7353154660035$$
$$x \geq -71.9446304817941 \wedge x \leq -61.6484065733173$$
$$x \geq -59.9535607517084 \wedge x \leq -57.6296158327081$$
$$x \geq -49.4130262826674 \wedge x \leq -47.8674926836918$$
$$x \geq -45.7553208896104 \wedge x \leq -35.7814970140969$$
$$x \geq -33.8796199609159 \wedge x \leq -23.6954544888424$$
$$x \geq -19.4587884353761 \wedge x \leq -11.6114441043886$$
$$x \geq -9.92049181202345 \wedge x \leq -7.69765946779217$$
$$x \geq 0.0259969878312562 \wedge x \leq 5.30170266613166$$
$$x \geq 14.2557271704627 \wedge x \leq 15.9671278777495$$
$$x \geq 26.3451765828346 \wedge x \leq 28.0383674979943$$
$$x \geq 38.5957978455979 \wedge x \leq 40.1269090033684$$
$$x \geq 42.2523150363882 \wedge x \leq 52.2132777167091$$
$$x \geq 54.128574941131 \wedge x \leq 64.2998397574696$$
$$x \geq 68.5297227402575 \wedge x \leq 76.3874647847242$$
$$x \geq 78.081604889231 \wedge x \leq 80.3190541652628$$
$$x \geq 88.519795836584 \wedge x \leq 90.1676573854581$$
$$x \geq 92.1945249026872 \wedge x \leq 92.7122815315705$$
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\left(\cos{\left(x \right)} + \cos^{2}{\left(\pi x \right)}\right) + \frac{2 \sin^{\sqrt{\frac{11}{5}}}{\left(\frac{x}{2} \right)}}{2} \right)} \geq 2$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\left(\cos{\left(x \right)} + \cos^{2}{\left(\pi x \right)}\right) + \frac{2 \sin^{\sqrt{\frac{11}{5}}}{\left(\frac{x}{2} \right)}}{2} \right)} = 2$$
Resolvemos:
$$x_{1} = 100.510435418134 - 0.0047674147312816 i$$
$$x_{2} = 68.5297227402575$$
$$x_{3} = -93.6529547362519 - 0.0504357558232563 i$$
$$x_{4} = 52.2132777167091$$
$$x_{5} = 94.4430446648741 + 0.0239734809090849 i$$
$$x_{6} = 40.1269090033684$$
$$x_{7} = -33.8796199609159$$
$$x_{8} = 8.08522178928987 + 0.221804327440013 i$$
$$x_{9} = 42.2523150363882$$
$$x_{10} = -87.4951623536677 + 0.0264918224471817 i$$
$$x_{11} = -61.6484065733173$$
$$x_{12} = -67.8271064885251 - 0.116532580524128 i$$
$$x_{13} = -41.919402019937 + 0.253793657662776 i$$
$$x_{14} = -83.8209630426373$$
$$x_{15} = -47.8674926836918$$
$$x_{16} = 90.1676573854581$$
$$x_{17} = -16.9160112621997 + 0.236091194526466 i$$
$$x_{18} = -7.69765946779217$$
$$x_{19} = 0.0259969878312562$$
$$x_{20} = 58.1159652901164 - 0.168943046399089 i$$
$$x_{21} = 28.0383674979943$$
$$x_{22} = 44.3912217448768 - 0.0386843113446253 i$$
$$x_{23} = 14.2557271704627$$
$$x_{24} = -57.6296158327081$$
$$x_{25} = -95.3640346092024$$
$$x_{26} = -95.6965840882506$$
$$x_{27} = 73.8767048669985 + 0.159634370423093 i$$
$$x_{28} = 56.5037427905596 + 0.0142885202923343 i$$
$$x_{29} = -5.66932787023074 - 0.0497064137401943 i$$
$$x_{30} = 88.519795836584$$
$$x_{31} = 26.3451765828346$$
$$x_{32} = -71.9446304817941$$
$$x_{33} = 92.1945249026872$$
$$x_{34} = 54.128574941131$$
$$x_{35} = -81.5428971975277 - 0.0191245612540122 i$$
$$x_{36} = 15.9671278777495$$
$$x_{37} = 80.3190541652628$$
$$x_{38} = -73.7353154660035$$
$$x_{39} = 64.2998397574696$$
$$x_{40} = 35.9079872393627 - 0.212205057974673 i$$
$$x_{41} = -52.089956603758 - 0.217871757172483 i$$
$$x_{42} = 32.2802458587386 - 0.0691505085823875 i$$
$$x_{43} = -66.9212508083606 + 0.269489880500199 i$$
$$x_{44} = 20.164782218209 - 0.121405581267706 i$$
$$x_{45} = 92.7122815315705$$
$$x_{46} = -99.6012951400255$$
$$x_{47} = 6.38590519069954 - 0.00575895418760668 i$$
$$x_{48} = -54.8953300391768 - 0.186195356732807 i$$
$$x_{49} = -31.4961106304242 - 0.0191707060545047 i$$
$$x_{50} = -14.1170844576311 - 0.166541967937758 i$$
$$x_{51} = -23.6954544888424$$
$$x_{52} = 82.3332156159097 - 0.0540938198971391 i$$
$$x_{53} = -29.8795040594379 - 0.162851569333039 i$$
$$x_{54} = -2.07254282841937 - 0.270802694872933 i$$
$$x_{55} = -17.7742905308476 - 0.0886248084834091 i$$
$$x_{56} = -19.4587884353761$$
$$x_{57} = -59.9535607517084$$
$$x_{58} = -45.7553208896104$$
$$x_{59} = 111.823557484907 + 0.114305309917005 i$$
$$x_{60} = 50.4985071395553 - 0.0369607780358167 i$$
$$x_{61} = 76.3874647847242$$
$$x_{62} = -35.7814970140969$$
$$x_{63} = 11.7207671633765 - 0.0672315020436625 i$$
$$x_{64} = -49.4130262826674$$
$$x_{65} = -75.4734559804639 - 0.0125866265148061 i$$
$$x_{66} = 3.28658644133219 - 0.369342697073948 i$$
$$x_{67} = 38.5957978455979$$
$$x_{68} = 5.30170266613166$$
$$x_{69} = -9.92049181202345$$
$$x_{70} = 85.9189522586373 - 0.251433509912749 i$$
$$x_{71} = -25.4194772379531 - 0.0303405831403926 i$$
$$x_{72} = -55.7122976199228 - 0.0670079176742718 i$$
$$x_{73} = -37.5022710508658 + 0.0343942270405407 i$$
$$x_{74} = 18.4984592764267 - 0.0265263451148552 i$$
$$x_{75} = -43.6019102829849 - 0.0368709510682677 i$$
$$x_{76} = -11.6114441043886$$
$$x_{77} = -97.9075682228443$$
$$x_{78} = 70.2194936875721 - 0.0917905796213954 i$$
$$x_{79} = -80.7389286380715 + 0.075669195211865 i$$
$$x_{80} = -40.9095455028656 - 0.321103912982183 i$$
$$x_{81} = -85.8215792771042$$
$$x_{82} = 62.5726892695298 - 0.0287324695214719 i$$
$$x_{83} = 12.543766196288 - 0.00146153110638568 i$$
$$x_{84} = 78.081604889231$$
Descartamos las soluciones complejas:
$$x_{1} = 68.5297227402575$$
$$x_{2} = 52.2132777167091$$
$$x_{3} = 40.1269090033684$$
$$x_{4} = -33.8796199609159$$
$$x_{5} = 42.2523150363882$$
$$x_{6} = -61.6484065733173$$
$$x_{7} = -83.8209630426373$$
$$x_{8} = -47.8674926836918$$
$$x_{9} = 90.1676573854581$$
$$x_{10} = -7.69765946779217$$
$$x_{11} = 0.0259969878312562$$
$$x_{12} = 28.0383674979943$$
$$x_{13} = 14.2557271704627$$
$$x_{14} = -57.6296158327081$$
$$x_{15} = -95.3640346092024$$
$$x_{16} = -95.6965840882506$$
$$x_{17} = 88.519795836584$$
$$x_{18} = 26.3451765828346$$
$$x_{19} = -71.9446304817941$$
$$x_{20} = 92.1945249026872$$
$$x_{21} = 54.128574941131$$
$$x_{22} = 15.9671278777495$$
$$x_{23} = 80.3190541652628$$
$$x_{24} = -73.7353154660035$$
$$x_{25} = 64.2998397574696$$
$$x_{26} = 92.7122815315705$$
$$x_{27} = -99.6012951400255$$
$$x_{28} = -23.6954544888424$$
$$x_{29} = -19.4587884353761$$
$$x_{30} = -59.9535607517084$$
$$x_{31} = -45.7553208896104$$
$$x_{32} = 76.3874647847242$$
$$x_{33} = -35.7814970140969$$
$$x_{34} = -49.4130262826674$$
$$x_{35} = 38.5957978455979$$
$$x_{36} = 5.30170266613166$$
$$x_{37} = -9.92049181202345$$
$$x_{38} = -11.6114441043886$$
$$x_{39} = -97.9075682228443$$
$$x_{40} = -85.8215792771042$$
$$x_{41} = 78.081604889231$$
Las raíces dadas
$$x_{27} = -99.6012951400255$$
$$x_{39} = -97.9075682228443$$
$$x_{16} = -95.6965840882506$$
$$x_{15} = -95.3640346092024$$
$$x_{40} = -85.8215792771042$$
$$x_{7} = -83.8209630426373$$
$$x_{24} = -73.7353154660035$$
$$x_{19} = -71.9446304817941$$
$$x_{6} = -61.6484065733173$$
$$x_{30} = -59.9535607517084$$
$$x_{14} = -57.6296158327081$$
$$x_{34} = -49.4130262826674$$
$$x_{8} = -47.8674926836918$$
$$x_{31} = -45.7553208896104$$
$$x_{33} = -35.7814970140969$$
$$x_{4} = -33.8796199609159$$
$$x_{28} = -23.6954544888424$$
$$x_{29} = -19.4587884353761$$
$$x_{38} = -11.6114441043886$$
$$x_{37} = -9.92049181202345$$
$$x_{10} = -7.69765946779217$$
$$x_{11} = 0.0259969878312562$$
$$x_{36} = 5.30170266613166$$
$$x_{13} = 14.2557271704627$$
$$x_{22} = 15.9671278777495$$
$$x_{18} = 26.3451765828346$$
$$x_{12} = 28.0383674979943$$
$$x_{35} = 38.5957978455979$$
$$x_{3} = 40.1269090033684$$
$$x_{5} = 42.2523150363882$$
$$x_{2} = 52.2132777167091$$
$$x_{21} = 54.128574941131$$
$$x_{25} = 64.2998397574696$$
$$x_{1} = 68.5297227402575$$
$$x_{32} = 76.3874647847242$$
$$x_{41} = 78.081604889231$$
$$x_{23} = 80.3190541652628$$
$$x_{17} = 88.519795836584$$
$$x_{9} = 90.1676573854581$$
$$x_{20} = 92.1945249026872$$
$$x_{26} = 92.7122815315705$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{27}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{27} - \frac{1}{10}$$
=
$$-99.6012951400255 + - \frac{1}{10}$$
=
$$-99.7012951400255$$
lo sustituimos en la expresión
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\left(\cos{\left(x \right)} + \cos^{2}{\left(\pi x \right)}\right) + \frac{2 \sin^{\sqrt{\frac{11}{5}}}{\left(\frac{x}{2} \right)}}{2} \right)} \geq 2$$
$$\left(-99.7012951400255 - 3\right) \left(-99.7012951400255 - 1\right) \log{\left(\frac{2 \sin^{\sqrt{\frac{11}{5}}}{\left(- \frac{99.7012951400255}{2} \right)}}{2} + \left(\cos^{2}{\left(\left(-99.7012951400255\right) \pi \right)} + \cos{\left(-99.7012951400255 \right)}\right) \right)} \geq 2$$
/ ____ \
| \/ 55 |
| ------ | >= 2
| 5 2 |
10342.1534331586*log\0.675119406768933 + 0.403038827677351 + cos (1.70129514002545*pi)/ significa que una de las soluciones de nuestra ecuación será con:
$$x \leq -99.6012951400255$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------
x27 x39 x16 x15 x40 x7 x24 x19 x6 x30 x14 x34 x8 x31 x33 x4 x28 x29 x38 x37 x10 x11 x36 x13 x22 x18 x12 x35 x3 x5 x2 x21 x25 x1 x32 x41 x23 x17 x9 x20 x26Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \leq -99.6012951400255$$
$$x \geq -97.9075682228443 \wedge x \leq -95.6965840882506$$
$$x \geq -95.3640346092024 \wedge x \leq -85.8215792771042$$
$$x \geq -83.8209630426373 \wedge x \leq -73.7353154660035$$
$$x \geq -71.9446304817941 \wedge x \leq -61.6484065733173$$
$$x \geq -59.9535607517084 \wedge x \leq -57.6296158327081$$
$$x \geq -49.4130262826674 \wedge x \leq -47.8674926836918$$
$$x \geq -45.7553208896104 \wedge x \leq -35.7814970140969$$
$$x \geq -33.8796199609159 \wedge x \leq -23.6954544888424$$
$$x \geq -19.4587884353761 \wedge x \leq -11.6114441043886$$
$$x \geq -9.92049181202345 \wedge x \leq -7.69765946779217$$
$$x \geq 0.0259969878312562 \wedge x \leq 5.30170266613166$$
$$x \geq 14.2557271704627 \wedge x \leq 15.9671278777495$$
$$x \geq 26.3451765828346 \wedge x \leq 28.0383674979943$$
$$x \geq 38.5957978455979 \wedge x \leq 40.1269090033684$$
$$x \geq 42.2523150363882 \wedge x \leq 52.2132777167091$$
$$x \geq 54.128574941131 \wedge x \leq 64.2998397574696$$
$$x \geq 68.5297227402575 \wedge x \leq 76.3874647847242$$
$$x \geq 78.081604889231 \wedge x \leq 80.3190541652628$$
$$x \geq 88.519795836584 \wedge x \leq 90.1676573854581$$
$$x \geq 92.1945249026872 \wedge x \leq 92.7122815315705$$
Solución de la desigualdad en el gráfico