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- 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>=25/(1-x)-9
-
(x^2−64)(x^2+2x)>0
-
x^2-7x+8>0
-
x^2+7x+6>0
-
Expresiones idénticas
- (x- tres)*(x- uno)*lg(cos^ dos (pi*x)+ uno)< uno
- (x menos 3) multiplicar por (x menos 1) multiplicar por lg( coseno de al cuadrado ( número pi multiplicar por x) más 1) menos 1
- (x menos tres) multiplicar por (x menos uno) multiplicar por lg( coseno de en el grado dos ( número pi multiplicar por x) más uno) menos uno
- (x-3)*(x-1)*lg(cos2(pi*x)+1)<1
- x-3*x-1*lgcos2pi*x+1<1
- (x-3)*(x-1)*lg(cos²(pi*x)+1)<1
- (x-3)*(x-1)*lg(cos en el grado 2(pi*x)+1)<1
- (x-3)(x-1)lg(cos^2(pix)+1)<1
- (x-3)(x-1)lg(cos2(pix)+1)<1
- x-3x-1lgcos2pix+1<1
- x-3x-1lgcos^2pix+1<1
-
Expresiones semejantes
- (x-3)*(x+1)*lg(cos^2(pi*x)+1)<1
- (x+3)*(x-1)*lg(cos^2(pi*x)+1)<1
- (x-3)*(x-1)*lg(cos^2(pi*x)-1)<1
(x-3)*(x-1)*lg(cos^2(pi*x)+1)<1 desigualdades
Solución
Ha introducido
[src]
/ 2 \ (x - 3)*(x - 1)*log\cos (pi*x) + 1/ < 1
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\cos^{2}{\left(\pi x \right)} + 1 \right)} < 1$$
((x - 3)*(x - 1))*log(cos(pi*x)^2 + 1) < 1
Solución detallada
Se da la desigualdad:
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\cos^{2}{\left(\pi x \right)} + 1 \right)} < 1$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\cos^{2}{\left(\pi x \right)} + 1 \right)} = 1$$
Resolvemos:
$$x_{1} = -43.4930000007884$$
$$x_{2} = 16.5220150236887$$
$$x_{3} = 60.5054421461245$$
$$x_{4} = -11.4762598277865$$
$$x_{5} = -37.4919351346903$$
$$x_{6} = 76.5042730765805$$
$$x_{7} = 26.5130052018827$$
$$x_{8} = 36.5092310136237$$
$$x_{9} = -87.4964429164863$$
$$x_{10} = 22.515549444763$$
$$x_{11} = -95.4967348589978$$
$$x_{12} = -71.4956682628334$$
$$x_{13} = -25.4884061396744$$
$$x_{14} = 88.503680177377$$
$$x_{15} = -59.4948225385562$$
$$x_{16} = -17.483623102338$$
$$x_{17} = -79.4960936308264$$
$$x_{18} = 86.5037672965979$$
$$x_{19} = -29.4898823202659$$
$$x_{20} = -91.4965951351524$$
$$x_{21} = 30.5111770004532$$
$$x_{22} = -1.59555966379431$$
$$x_{23} = -89.4965206901481$$
$$x_{24} = 8.44952125053651$$
$$x_{25} = -45.4932950677941$$
$$x_{26} = 44.5074921261369$$
$$x_{27} = -63.4951389074941$$
$$x_{28} = 12.5304804726907$$
$$x_{29} = 34.5097997011727$$
$$x_{30} = 84.5038586408689$$
$$x_{31} = 54.5060643619126$$
$$x_{32} = 72.5045155774535$$
$$x_{33} = 14.5255626076169$$
$$x_{34} = 80.504055296772$$
$$x_{35} = -31.4904877363144$$
$$x_{36} = -73.4957830612624$$
$$x_{37} = -27.4891944845186$$
$$x_{38} = -39.4923243754472$$
$$x_{39} = -3.43958148804299$$
$$x_{40} = 0.221807963386119$$
$$x_{41} = -67.4954188301294$$
$$x_{42} = -15.4817370018211$$
$$x_{43} = 74.5043909810345$$
$$x_{44} = 90.5035969966717$$
$$x_{45} = -81.4961872301226$$
$$x_{46} = -19.4851551520666$$
$$x_{47} = 20.5172360632228$$
$$x_{48} = -21.4864244910587$$
$$x_{49} = 96.5033685842875$$
$$x_{50} = -49.4938163452292$$
$$x_{51} = 18.5193339823549$$
$$x_{52} = -9.47205817550102$$
$$x_{53} = 78.5041613390078$$
$$x_{54} = -55.494462106779$$
$$x_{55} = -75.4958919308556$$
$$x_{56} = 7.55903740770251$$
$$x_{57} = -93.4966664607468$$
$$x_{58} = 58.5056348594569$$
$$x_{59} = 50.5065647602729$$
$$x_{60} = 66.5049357468693$$
$$x_{61} = 40.5082711278866$$
$$x_{62} = 100.503231771756$$
$$x_{63} = -61.4949857097978$$
$$x_{64} = -69.4955470375819$$
$$x_{65} = -7.46602409795829$$
$$x_{66} = 48.5068472686294$$
$$x_{67} = 38.5087247370157$$
$$x_{68} = 10.5377604183289$$
$$x_{69} = 92.503517493286$$
$$x_{70} = -41.4926777502424$$
$$x_{71} = 98.5032987600018$$
$$x_{72} = 70.5046474522816$$
$$x_{73} = -5.45659003243077$$
$$x_{74} = 42.5078623713187$$
$$x_{75} = -77.4959953194362$$
$$x_{76} = 24.5141638429446$$
$$x_{77} = -99.4968635659973$$
$$x_{78} = 68.5047872625577$$
$$x_{79} = 4.64041391623721$$
$$x_{80} = 32.5104431060889$$
$$x_{81} = -47.4935662533316$$
$$x_{82} = -65.4952830191904$$
$$x_{83} = -13.4793573719887$$
$$x_{84} = 3.77819203661388$$
$$x_{85} = -53.4942623856679$$
$$x_{86} = -23.4874934740191$$
$$x_{87} = 94.5034414286219$$
$$x_{88} = 62.5052621806364$$
$$x_{89} = -83.49627644823$$
$$x_{90} = -35.4915042706539$$
$$x_{91} = -57.4946483866948$$
$$x_{92} = 64.5050937384109$$
$$x_{93} = 52.5063046452329$$
$$x_{94} = -33.4910247228418$$
$$x_{95} = 28.5120219354654$$
$$x_{96} = 56.505841725139$$
$$x_{97} = -97.4968005065196$$
$$x_{98} = -51.4940477134676$$
$$x_{99} = 82.503954525213$$
$$x_{100} = -85.4963615857739$$
$$x_{101} = 46.5071551930507$$
$$x_{1} = -43.4930000007884$$
$$x_{2} = 16.5220150236887$$
$$x_{3} = 60.5054421461245$$
$$x_{4} = -11.4762598277865$$
$$x_{5} = -37.4919351346903$$
$$x_{6} = 76.5042730765805$$
$$x_{7} = 26.5130052018827$$
$$x_{8} = 36.5092310136237$$
$$x_{9} = -87.4964429164863$$
$$x_{10} = 22.515549444763$$
$$x_{11} = -95.4967348589978$$
$$x_{12} = -71.4956682628334$$
$$x_{13} = -25.4884061396744$$
$$x_{14} = 88.503680177377$$
$$x_{15} = -59.4948225385562$$
$$x_{16} = -17.483623102338$$
$$x_{17} = -79.4960936308264$$
$$x_{18} = 86.5037672965979$$
$$x_{19} = -29.4898823202659$$
$$x_{20} = -91.4965951351524$$
$$x_{21} = 30.5111770004532$$
$$x_{22} = -1.59555966379431$$
$$x_{23} = -89.4965206901481$$
$$x_{24} = 8.44952125053651$$
$$x_{25} = -45.4932950677941$$
$$x_{26} = 44.5074921261369$$
$$x_{27} = -63.4951389074941$$
$$x_{28} = 12.5304804726907$$
$$x_{29} = 34.5097997011727$$
$$x_{30} = 84.5038586408689$$
$$x_{31} = 54.5060643619126$$
$$x_{32} = 72.5045155774535$$
$$x_{33} = 14.5255626076169$$
$$x_{34} = 80.504055296772$$
$$x_{35} = -31.4904877363144$$
$$x_{36} = -73.4957830612624$$
$$x_{37} = -27.4891944845186$$
$$x_{38} = -39.4923243754472$$
$$x_{39} = -3.43958148804299$$
$$x_{40} = 0.221807963386119$$
$$x_{41} = -67.4954188301294$$
$$x_{42} = -15.4817370018211$$
$$x_{43} = 74.5043909810345$$
$$x_{44} = 90.5035969966717$$
$$x_{45} = -81.4961872301226$$
$$x_{46} = -19.4851551520666$$
$$x_{47} = 20.5172360632228$$
$$x_{48} = -21.4864244910587$$
$$x_{49} = 96.5033685842875$$
$$x_{50} = -49.4938163452292$$
$$x_{51} = 18.5193339823549$$
$$x_{52} = -9.47205817550102$$
$$x_{53} = 78.5041613390078$$
$$x_{54} = -55.494462106779$$
$$x_{55} = -75.4958919308556$$
$$x_{56} = 7.55903740770251$$
$$x_{57} = -93.4966664607468$$
$$x_{58} = 58.5056348594569$$
$$x_{59} = 50.5065647602729$$
$$x_{60} = 66.5049357468693$$
$$x_{61} = 40.5082711278866$$
$$x_{62} = 100.503231771756$$
$$x_{63} = -61.4949857097978$$
$$x_{64} = -69.4955470375819$$
$$x_{65} = -7.46602409795829$$
$$x_{66} = 48.5068472686294$$
$$x_{67} = 38.5087247370157$$
$$x_{68} = 10.5377604183289$$
$$x_{69} = 92.503517493286$$
$$x_{70} = -41.4926777502424$$
$$x_{71} = 98.5032987600018$$
$$x_{72} = 70.5046474522816$$
$$x_{73} = -5.45659003243077$$
$$x_{74} = 42.5078623713187$$
$$x_{75} = -77.4959953194362$$
$$x_{76} = 24.5141638429446$$
$$x_{77} = -99.4968635659973$$
$$x_{78} = 68.5047872625577$$
$$x_{79} = 4.64041391623721$$
$$x_{80} = 32.5104431060889$$
$$x_{81} = -47.4935662533316$$
$$x_{82} = -65.4952830191904$$
$$x_{83} = -13.4793573719887$$
$$x_{84} = 3.77819203661388$$
$$x_{85} = -53.4942623856679$$
$$x_{86} = -23.4874934740191$$
$$x_{87} = 94.5034414286219$$
$$x_{88} = 62.5052621806364$$
$$x_{89} = -83.49627644823$$
$$x_{90} = -35.4915042706539$$
$$x_{91} = -57.4946483866948$$
$$x_{92} = 64.5050937384109$$
$$x_{93} = 52.5063046452329$$
$$x_{94} = -33.4910247228418$$
$$x_{95} = 28.5120219354654$$
$$x_{96} = 56.505841725139$$
$$x_{97} = -97.4968005065196$$
$$x_{98} = -51.4940477134676$$
$$x_{99} = 82.503954525213$$
$$x_{100} = -85.4963615857739$$
$$x_{101} = 46.5071551930507$$
Las raíces dadas
$$x_{77} = -99.4968635659973$$
$$x_{97} = -97.4968005065196$$
$$x_{11} = -95.4967348589978$$
$$x_{57} = -93.4966664607468$$
$$x_{20} = -91.4965951351524$$
$$x_{23} = -89.4965206901481$$
$$x_{9} = -87.4964429164863$$
$$x_{100} = -85.4963615857739$$
$$x_{89} = -83.49627644823$$
$$x_{45} = -81.4961872301226$$
$$x_{17} = -79.4960936308264$$
$$x_{75} = -77.4959953194362$$
$$x_{55} = -75.4958919308556$$
$$x_{36} = -73.4957830612624$$
$$x_{12} = -71.4956682628334$$
$$x_{64} = -69.4955470375819$$
$$x_{41} = -67.4954188301294$$
$$x_{82} = -65.4952830191904$$
$$x_{27} = -63.4951389074941$$
$$x_{63} = -61.4949857097978$$
$$x_{15} = -59.4948225385562$$
$$x_{91} = -57.4946483866948$$
$$x_{54} = -55.494462106779$$
$$x_{85} = -53.4942623856679$$
$$x_{98} = -51.4940477134676$$
$$x_{50} = -49.4938163452292$$
$$x_{81} = -47.4935662533316$$
$$x_{25} = -45.4932950677941$$
$$x_{1} = -43.4930000007884$$
$$x_{70} = -41.4926777502424$$
$$x_{38} = -39.4923243754472$$
$$x_{5} = -37.4919351346903$$
$$x_{90} = -35.4915042706539$$
$$x_{94} = -33.4910247228418$$
$$x_{35} = -31.4904877363144$$
$$x_{19} = -29.4898823202659$$
$$x_{37} = -27.4891944845186$$
$$x_{13} = -25.4884061396744$$
$$x_{86} = -23.4874934740191$$
$$x_{48} = -21.4864244910587$$
$$x_{46} = -19.4851551520666$$
$$x_{16} = -17.483623102338$$
$$x_{42} = -15.4817370018211$$
$$x_{83} = -13.4793573719887$$
$$x_{4} = -11.4762598277865$$
$$x_{52} = -9.47205817550102$$
$$x_{65} = -7.46602409795829$$
$$x_{73} = -5.45659003243077$$
$$x_{39} = -3.43958148804299$$
$$x_{22} = -1.59555966379431$$
$$x_{40} = 0.221807963386119$$
$$x_{84} = 3.77819203661388$$
$$x_{79} = 4.64041391623721$$
$$x_{56} = 7.55903740770251$$
$$x_{24} = 8.44952125053651$$
$$x_{68} = 10.5377604183289$$
$$x_{28} = 12.5304804726907$$
$$x_{33} = 14.5255626076169$$
$$x_{2} = 16.5220150236887$$
$$x_{51} = 18.5193339823549$$
$$x_{47} = 20.5172360632228$$
$$x_{10} = 22.515549444763$$
$$x_{76} = 24.5141638429446$$
$$x_{7} = 26.5130052018827$$
$$x_{95} = 28.5120219354654$$
$$x_{21} = 30.5111770004532$$
$$x_{80} = 32.5104431060889$$
$$x_{29} = 34.5097997011727$$
$$x_{8} = 36.5092310136237$$
$$x_{67} = 38.5087247370157$$
$$x_{61} = 40.5082711278866$$
$$x_{74} = 42.5078623713187$$
$$x_{26} = 44.5074921261369$$
$$x_{101} = 46.5071551930507$$
$$x_{66} = 48.5068472686294$$
$$x_{59} = 50.5065647602729$$
$$x_{93} = 52.5063046452329$$
$$x_{31} = 54.5060643619126$$
$$x_{96} = 56.505841725139$$
$$x_{58} = 58.5056348594569$$
$$x_{3} = 60.5054421461245$$
$$x_{88} = 62.5052621806364$$
$$x_{92} = 64.5050937384109$$
$$x_{60} = 66.5049357468693$$
$$x_{78} = 68.5047872625577$$
$$x_{72} = 70.5046474522816$$
$$x_{32} = 72.5045155774535$$
$$x_{43} = 74.5043909810345$$
$$x_{6} = 76.5042730765805$$
$$x_{53} = 78.5041613390078$$
$$x_{34} = 80.504055296772$$
$$x_{99} = 82.503954525213$$
$$x_{30} = 84.5038586408689$$
$$x_{18} = 86.5037672965979$$
$$x_{14} = 88.503680177377$$
$$x_{44} = 90.5035969966717$$
$$x_{69} = 92.503517493286$$
$$x_{87} = 94.5034414286219$$
$$x_{49} = 96.5033685842875$$
$$x_{71} = 98.5032987600018$$
$$x_{62} = 100.503231771756$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{77}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{77} - \frac{1}{10}$$
=
$$-99.4968635659973 + - \frac{1}{10}$$
=
$$-99.5968635659973$$
lo sustituimos en la expresión
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\cos^{2}{\left(\pi x \right)} + 1 \right)} < 1$$
$$\left(-99.5968635659973 - 3\right) \left(-99.5968635659973 - 1\right) \log{\left(\cos^{2}{\left(\left(-99.5968635659973\right) \pi \right)} + 1 \right)} < 1$$
pero
Entonces
$$x < -99.4968635659973$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -99.4968635659973 \wedge x < -97.4968005065196$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -99.4968635659973 \wedge x < -97.4968005065196$$
$$x > -95.4967348589978 \wedge x < -93.4966664607468$$
$$x > -91.4965951351524 \wedge x < -89.4965206901481$$
$$x > -87.4964429164863 \wedge x < -85.4963615857739$$
$$x > -83.49627644823 \wedge x < -81.4961872301226$$
$$x > -79.4960936308264 \wedge x < -77.4959953194362$$
$$x > -75.4958919308556 \wedge x < -73.4957830612624$$
$$x > -71.4956682628334 \wedge x < -69.4955470375819$$
$$x > -67.4954188301294 \wedge x < -65.4952830191904$$
$$x > -63.4951389074941 \wedge x < -61.4949857097978$$
$$x > -59.4948225385562 \wedge x < -57.4946483866948$$
$$x > -55.494462106779 \wedge x < -53.4942623856679$$
$$x > -51.4940477134676 \wedge x < -49.4938163452292$$
$$x > -47.4935662533316 \wedge x < -45.4932950677941$$
$$x > -43.4930000007884 \wedge x < -41.4926777502424$$
$$x > -39.4923243754472 \wedge x < -37.4919351346903$$
$$x > -35.4915042706539 \wedge x < -33.4910247228418$$
$$x > -31.4904877363144 \wedge x < -29.4898823202659$$
$$x > -27.4891944845186 \wedge x < -25.4884061396744$$
$$x > -23.4874934740191 \wedge x < -21.4864244910587$$
$$x > -19.4851551520666 \wedge x < -17.483623102338$$
$$x > -15.4817370018211 \wedge x < -13.4793573719887$$
$$x > -11.4762598277865 \wedge x < -9.47205817550102$$
$$x > -7.46602409795829 \wedge x < -5.45659003243077$$
$$x > -3.43958148804299 \wedge x < -1.59555966379431$$
$$x > 0.221807963386119 \wedge x < 3.77819203661388$$
$$x > 4.64041391623721 \wedge x < 7.55903740770251$$
$$x > 8.44952125053651 \wedge x < 10.5377604183289$$
$$x > 12.5304804726907 \wedge x < 14.5255626076169$$
$$x > 16.5220150236887 \wedge x < 18.5193339823549$$
$$x > 20.5172360632228 \wedge x < 22.515549444763$$
$$x > 24.5141638429446 \wedge x < 26.5130052018827$$
$$x > 28.5120219354654 \wedge x < 30.5111770004532$$
$$x > 32.5104431060889 \wedge x < 34.5097997011727$$
$$x > 36.5092310136237 \wedge x < 38.5087247370157$$
$$x > 40.5082711278866 \wedge x < 42.5078623713187$$
$$x > 44.5074921261369 \wedge x < 46.5071551930507$$
$$x > 48.5068472686294 \wedge x < 50.5065647602729$$
$$x > 52.5063046452329 \wedge x < 54.5060643619126$$
$$x > 56.505841725139 \wedge x < 58.5056348594569$$
$$x > 60.5054421461245 \wedge x < 62.5052621806364$$
$$x > 64.5050937384109 \wedge x < 66.5049357468693$$
$$x > 68.5047872625577 \wedge x < 70.5046474522816$$
$$x > 72.5045155774535 \wedge x < 74.5043909810345$$
$$x > 76.5042730765805 \wedge x < 78.5041613390078$$
$$x > 80.504055296772 \wedge x < 82.503954525213$$
$$x > 84.5038586408689 \wedge x < 86.5037672965979$$
$$x > 88.503680177377 \wedge x < 90.5035969966717$$
$$x > 92.503517493286 \wedge x < 94.5034414286219$$
$$x > 96.5033685842875 \wedge x < 98.5032987600018$$
$$x > 100.503231771756$$
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\cos^{2}{\left(\pi x \right)} + 1 \right)} < 1$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\cos^{2}{\left(\pi x \right)} + 1 \right)} = 1$$
Resolvemos:
$$x_{1} = -43.4930000007884$$
$$x_{2} = 16.5220150236887$$
$$x_{3} = 60.5054421461245$$
$$x_{4} = -11.4762598277865$$
$$x_{5} = -37.4919351346903$$
$$x_{6} = 76.5042730765805$$
$$x_{7} = 26.5130052018827$$
$$x_{8} = 36.5092310136237$$
$$x_{9} = -87.4964429164863$$
$$x_{10} = 22.515549444763$$
$$x_{11} = -95.4967348589978$$
$$x_{12} = -71.4956682628334$$
$$x_{13} = -25.4884061396744$$
$$x_{14} = 88.503680177377$$
$$x_{15} = -59.4948225385562$$
$$x_{16} = -17.483623102338$$
$$x_{17} = -79.4960936308264$$
$$x_{18} = 86.5037672965979$$
$$x_{19} = -29.4898823202659$$
$$x_{20} = -91.4965951351524$$
$$x_{21} = 30.5111770004532$$
$$x_{22} = -1.59555966379431$$
$$x_{23} = -89.4965206901481$$
$$x_{24} = 8.44952125053651$$
$$x_{25} = -45.4932950677941$$
$$x_{26} = 44.5074921261369$$
$$x_{27} = -63.4951389074941$$
$$x_{28} = 12.5304804726907$$
$$x_{29} = 34.5097997011727$$
$$x_{30} = 84.5038586408689$$
$$x_{31} = 54.5060643619126$$
$$x_{32} = 72.5045155774535$$
$$x_{33} = 14.5255626076169$$
$$x_{34} = 80.504055296772$$
$$x_{35} = -31.4904877363144$$
$$x_{36} = -73.4957830612624$$
$$x_{37} = -27.4891944845186$$
$$x_{38} = -39.4923243754472$$
$$x_{39} = -3.43958148804299$$
$$x_{40} = 0.221807963386119$$
$$x_{41} = -67.4954188301294$$
$$x_{42} = -15.4817370018211$$
$$x_{43} = 74.5043909810345$$
$$x_{44} = 90.5035969966717$$
$$x_{45} = -81.4961872301226$$
$$x_{46} = -19.4851551520666$$
$$x_{47} = 20.5172360632228$$
$$x_{48} = -21.4864244910587$$
$$x_{49} = 96.5033685842875$$
$$x_{50} = -49.4938163452292$$
$$x_{51} = 18.5193339823549$$
$$x_{52} = -9.47205817550102$$
$$x_{53} = 78.5041613390078$$
$$x_{54} = -55.494462106779$$
$$x_{55} = -75.4958919308556$$
$$x_{56} = 7.55903740770251$$
$$x_{57} = -93.4966664607468$$
$$x_{58} = 58.5056348594569$$
$$x_{59} = 50.5065647602729$$
$$x_{60} = 66.5049357468693$$
$$x_{61} = 40.5082711278866$$
$$x_{62} = 100.503231771756$$
$$x_{63} = -61.4949857097978$$
$$x_{64} = -69.4955470375819$$
$$x_{65} = -7.46602409795829$$
$$x_{66} = 48.5068472686294$$
$$x_{67} = 38.5087247370157$$
$$x_{68} = 10.5377604183289$$
$$x_{69} = 92.503517493286$$
$$x_{70} = -41.4926777502424$$
$$x_{71} = 98.5032987600018$$
$$x_{72} = 70.5046474522816$$
$$x_{73} = -5.45659003243077$$
$$x_{74} = 42.5078623713187$$
$$x_{75} = -77.4959953194362$$
$$x_{76} = 24.5141638429446$$
$$x_{77} = -99.4968635659973$$
$$x_{78} = 68.5047872625577$$
$$x_{79} = 4.64041391623721$$
$$x_{80} = 32.5104431060889$$
$$x_{81} = -47.4935662533316$$
$$x_{82} = -65.4952830191904$$
$$x_{83} = -13.4793573719887$$
$$x_{84} = 3.77819203661388$$
$$x_{85} = -53.4942623856679$$
$$x_{86} = -23.4874934740191$$
$$x_{87} = 94.5034414286219$$
$$x_{88} = 62.5052621806364$$
$$x_{89} = -83.49627644823$$
$$x_{90} = -35.4915042706539$$
$$x_{91} = -57.4946483866948$$
$$x_{92} = 64.5050937384109$$
$$x_{93} = 52.5063046452329$$
$$x_{94} = -33.4910247228418$$
$$x_{95} = 28.5120219354654$$
$$x_{96} = 56.505841725139$$
$$x_{97} = -97.4968005065196$$
$$x_{98} = -51.4940477134676$$
$$x_{99} = 82.503954525213$$
$$x_{100} = -85.4963615857739$$
$$x_{101} = 46.5071551930507$$
$$x_{1} = -43.4930000007884$$
$$x_{2} = 16.5220150236887$$
$$x_{3} = 60.5054421461245$$
$$x_{4} = -11.4762598277865$$
$$x_{5} = -37.4919351346903$$
$$x_{6} = 76.5042730765805$$
$$x_{7} = 26.5130052018827$$
$$x_{8} = 36.5092310136237$$
$$x_{9} = -87.4964429164863$$
$$x_{10} = 22.515549444763$$
$$x_{11} = -95.4967348589978$$
$$x_{12} = -71.4956682628334$$
$$x_{13} = -25.4884061396744$$
$$x_{14} = 88.503680177377$$
$$x_{15} = -59.4948225385562$$
$$x_{16} = -17.483623102338$$
$$x_{17} = -79.4960936308264$$
$$x_{18} = 86.5037672965979$$
$$x_{19} = -29.4898823202659$$
$$x_{20} = -91.4965951351524$$
$$x_{21} = 30.5111770004532$$
$$x_{22} = -1.59555966379431$$
$$x_{23} = -89.4965206901481$$
$$x_{24} = 8.44952125053651$$
$$x_{25} = -45.4932950677941$$
$$x_{26} = 44.5074921261369$$
$$x_{27} = -63.4951389074941$$
$$x_{28} = 12.5304804726907$$
$$x_{29} = 34.5097997011727$$
$$x_{30} = 84.5038586408689$$
$$x_{31} = 54.5060643619126$$
$$x_{32} = 72.5045155774535$$
$$x_{33} = 14.5255626076169$$
$$x_{34} = 80.504055296772$$
$$x_{35} = -31.4904877363144$$
$$x_{36} = -73.4957830612624$$
$$x_{37} = -27.4891944845186$$
$$x_{38} = -39.4923243754472$$
$$x_{39} = -3.43958148804299$$
$$x_{40} = 0.221807963386119$$
$$x_{41} = -67.4954188301294$$
$$x_{42} = -15.4817370018211$$
$$x_{43} = 74.5043909810345$$
$$x_{44} = 90.5035969966717$$
$$x_{45} = -81.4961872301226$$
$$x_{46} = -19.4851551520666$$
$$x_{47} = 20.5172360632228$$
$$x_{48} = -21.4864244910587$$
$$x_{49} = 96.5033685842875$$
$$x_{50} = -49.4938163452292$$
$$x_{51} = 18.5193339823549$$
$$x_{52} = -9.47205817550102$$
$$x_{53} = 78.5041613390078$$
$$x_{54} = -55.494462106779$$
$$x_{55} = -75.4958919308556$$
$$x_{56} = 7.55903740770251$$
$$x_{57} = -93.4966664607468$$
$$x_{58} = 58.5056348594569$$
$$x_{59} = 50.5065647602729$$
$$x_{60} = 66.5049357468693$$
$$x_{61} = 40.5082711278866$$
$$x_{62} = 100.503231771756$$
$$x_{63} = -61.4949857097978$$
$$x_{64} = -69.4955470375819$$
$$x_{65} = -7.46602409795829$$
$$x_{66} = 48.5068472686294$$
$$x_{67} = 38.5087247370157$$
$$x_{68} = 10.5377604183289$$
$$x_{69} = 92.503517493286$$
$$x_{70} = -41.4926777502424$$
$$x_{71} = 98.5032987600018$$
$$x_{72} = 70.5046474522816$$
$$x_{73} = -5.45659003243077$$
$$x_{74} = 42.5078623713187$$
$$x_{75} = -77.4959953194362$$
$$x_{76} = 24.5141638429446$$
$$x_{77} = -99.4968635659973$$
$$x_{78} = 68.5047872625577$$
$$x_{79} = 4.64041391623721$$
$$x_{80} = 32.5104431060889$$
$$x_{81} = -47.4935662533316$$
$$x_{82} = -65.4952830191904$$
$$x_{83} = -13.4793573719887$$
$$x_{84} = 3.77819203661388$$
$$x_{85} = -53.4942623856679$$
$$x_{86} = -23.4874934740191$$
$$x_{87} = 94.5034414286219$$
$$x_{88} = 62.5052621806364$$
$$x_{89} = -83.49627644823$$
$$x_{90} = -35.4915042706539$$
$$x_{91} = -57.4946483866948$$
$$x_{92} = 64.5050937384109$$
$$x_{93} = 52.5063046452329$$
$$x_{94} = -33.4910247228418$$
$$x_{95} = 28.5120219354654$$
$$x_{96} = 56.505841725139$$
$$x_{97} = -97.4968005065196$$
$$x_{98} = -51.4940477134676$$
$$x_{99} = 82.503954525213$$
$$x_{100} = -85.4963615857739$$
$$x_{101} = 46.5071551930507$$
Las raíces dadas
$$x_{77} = -99.4968635659973$$
$$x_{97} = -97.4968005065196$$
$$x_{11} = -95.4967348589978$$
$$x_{57} = -93.4966664607468$$
$$x_{20} = -91.4965951351524$$
$$x_{23} = -89.4965206901481$$
$$x_{9} = -87.4964429164863$$
$$x_{100} = -85.4963615857739$$
$$x_{89} = -83.49627644823$$
$$x_{45} = -81.4961872301226$$
$$x_{17} = -79.4960936308264$$
$$x_{75} = -77.4959953194362$$
$$x_{55} = -75.4958919308556$$
$$x_{36} = -73.4957830612624$$
$$x_{12} = -71.4956682628334$$
$$x_{64} = -69.4955470375819$$
$$x_{41} = -67.4954188301294$$
$$x_{82} = -65.4952830191904$$
$$x_{27} = -63.4951389074941$$
$$x_{63} = -61.4949857097978$$
$$x_{15} = -59.4948225385562$$
$$x_{91} = -57.4946483866948$$
$$x_{54} = -55.494462106779$$
$$x_{85} = -53.4942623856679$$
$$x_{98} = -51.4940477134676$$
$$x_{50} = -49.4938163452292$$
$$x_{81} = -47.4935662533316$$
$$x_{25} = -45.4932950677941$$
$$x_{1} = -43.4930000007884$$
$$x_{70} = -41.4926777502424$$
$$x_{38} = -39.4923243754472$$
$$x_{5} = -37.4919351346903$$
$$x_{90} = -35.4915042706539$$
$$x_{94} = -33.4910247228418$$
$$x_{35} = -31.4904877363144$$
$$x_{19} = -29.4898823202659$$
$$x_{37} = -27.4891944845186$$
$$x_{13} = -25.4884061396744$$
$$x_{86} = -23.4874934740191$$
$$x_{48} = -21.4864244910587$$
$$x_{46} = -19.4851551520666$$
$$x_{16} = -17.483623102338$$
$$x_{42} = -15.4817370018211$$
$$x_{83} = -13.4793573719887$$
$$x_{4} = -11.4762598277865$$
$$x_{52} = -9.47205817550102$$
$$x_{65} = -7.46602409795829$$
$$x_{73} = -5.45659003243077$$
$$x_{39} = -3.43958148804299$$
$$x_{22} = -1.59555966379431$$
$$x_{40} = 0.221807963386119$$
$$x_{84} = 3.77819203661388$$
$$x_{79} = 4.64041391623721$$
$$x_{56} = 7.55903740770251$$
$$x_{24} = 8.44952125053651$$
$$x_{68} = 10.5377604183289$$
$$x_{28} = 12.5304804726907$$
$$x_{33} = 14.5255626076169$$
$$x_{2} = 16.5220150236887$$
$$x_{51} = 18.5193339823549$$
$$x_{47} = 20.5172360632228$$
$$x_{10} = 22.515549444763$$
$$x_{76} = 24.5141638429446$$
$$x_{7} = 26.5130052018827$$
$$x_{95} = 28.5120219354654$$
$$x_{21} = 30.5111770004532$$
$$x_{80} = 32.5104431060889$$
$$x_{29} = 34.5097997011727$$
$$x_{8} = 36.5092310136237$$
$$x_{67} = 38.5087247370157$$
$$x_{61} = 40.5082711278866$$
$$x_{74} = 42.5078623713187$$
$$x_{26} = 44.5074921261369$$
$$x_{101} = 46.5071551930507$$
$$x_{66} = 48.5068472686294$$
$$x_{59} = 50.5065647602729$$
$$x_{93} = 52.5063046452329$$
$$x_{31} = 54.5060643619126$$
$$x_{96} = 56.505841725139$$
$$x_{58} = 58.5056348594569$$
$$x_{3} = 60.5054421461245$$
$$x_{88} = 62.5052621806364$$
$$x_{92} = 64.5050937384109$$
$$x_{60} = 66.5049357468693$$
$$x_{78} = 68.5047872625577$$
$$x_{72} = 70.5046474522816$$
$$x_{32} = 72.5045155774535$$
$$x_{43} = 74.5043909810345$$
$$x_{6} = 76.5042730765805$$
$$x_{53} = 78.5041613390078$$
$$x_{34} = 80.504055296772$$
$$x_{99} = 82.503954525213$$
$$x_{30} = 84.5038586408689$$
$$x_{18} = 86.5037672965979$$
$$x_{14} = 88.503680177377$$
$$x_{44} = 90.5035969966717$$
$$x_{69} = 92.503517493286$$
$$x_{87} = 94.5034414286219$$
$$x_{49} = 96.5033685842875$$
$$x_{71} = 98.5032987600018$$
$$x_{62} = 100.503231771756$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{77}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{77} - \frac{1}{10}$$
=
$$-99.4968635659973 + - \frac{1}{10}$$
=
$$-99.5968635659973$$
lo sustituimos en la expresión
$$\left(x - 3\right) \left(x - 1\right) \log{\left(\cos^{2}{\left(\pi x \right)} + 1 \right)} < 1$$
$$\left(-99.5968635659973 - 3\right) \left(-99.5968635659973 - 1\right) \log{\left(\cos^{2}{\left(\left(-99.5968635659973\right) \pi \right)} + 1 \right)} < 1$$
/ 2 \
10320.9226864479*log\1 + cos (1.59686356599732*pi)/ < 1
pero
/ 2 \
10320.9226864479*log\1 + cos (1.59686356599732*pi)/ > 1
Entonces
$$x < -99.4968635659973$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -99.4968635659973 \wedge x < -97.4968005065196$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------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-------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-------
x77 x97 x11 x57 x20 x23 x9 x100 x89 x45 x17 x75 x55 x36 x12 x64 x41 x82 x27 x63 x15 x91 x54 x85 x98 x50 x81 x25 x1 x70 x38 x5 x90 x94 x35 x19 x37 x13 x86 x48 x46 x16 x42 x83 x4 x52 x65 x73 x39 x22 x40 x84 x79 x56 x24 x68 x28 x33 x2 x51 x47 x10 x76 x7 x95 x21 x80 x29 x8 x67 x61 x74 x26 x101 x66 x59 x93 x31 x96 x58 x3 x88 x92 x60 x78 x72 x32 x43 x6 x53 x34 x99 x30 x18 x14 x44 x69 x87 x49 x71 x62Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -99.4968635659973 \wedge x < -97.4968005065196$$
$$x > -95.4967348589978 \wedge x < -93.4966664607468$$
$$x > -91.4965951351524 \wedge x < -89.4965206901481$$
$$x > -87.4964429164863 \wedge x < -85.4963615857739$$
$$x > -83.49627644823 \wedge x < -81.4961872301226$$
$$x > -79.4960936308264 \wedge x < -77.4959953194362$$
$$x > -75.4958919308556 \wedge x < -73.4957830612624$$
$$x > -71.4956682628334 \wedge x < -69.4955470375819$$
$$x > -67.4954188301294 \wedge x < -65.4952830191904$$
$$x > -63.4951389074941 \wedge x < -61.4949857097978$$
$$x > -59.4948225385562 \wedge x < -57.4946483866948$$
$$x > -55.494462106779 \wedge x < -53.4942623856679$$
$$x > -51.4940477134676 \wedge x < -49.4938163452292$$
$$x > -47.4935662533316 \wedge x < -45.4932950677941$$
$$x > -43.4930000007884 \wedge x < -41.4926777502424$$
$$x > -39.4923243754472 \wedge x < -37.4919351346903$$
$$x > -35.4915042706539 \wedge x < -33.4910247228418$$
$$x > -31.4904877363144 \wedge x < -29.4898823202659$$
$$x > -27.4891944845186 \wedge x < -25.4884061396744$$
$$x > -23.4874934740191 \wedge x < -21.4864244910587$$
$$x > -19.4851551520666 \wedge x < -17.483623102338$$
$$x > -15.4817370018211 \wedge x < -13.4793573719887$$
$$x > -11.4762598277865 \wedge x < -9.47205817550102$$
$$x > -7.46602409795829 \wedge x < -5.45659003243077$$
$$x > -3.43958148804299 \wedge x < -1.59555966379431$$
$$x > 0.221807963386119 \wedge x < 3.77819203661388$$
$$x > 4.64041391623721 \wedge x < 7.55903740770251$$
$$x > 8.44952125053651 \wedge x < 10.5377604183289$$
$$x > 12.5304804726907 \wedge x < 14.5255626076169$$
$$x > 16.5220150236887 \wedge x < 18.5193339823549$$
$$x > 20.5172360632228 \wedge x < 22.515549444763$$
$$x > 24.5141638429446 \wedge x < 26.5130052018827$$
$$x > 28.5120219354654 \wedge x < 30.5111770004532$$
$$x > 32.5104431060889 \wedge x < 34.5097997011727$$
$$x > 36.5092310136237 \wedge x < 38.5087247370157$$
$$x > 40.5082711278866 \wedge x < 42.5078623713187$$
$$x > 44.5074921261369 \wedge x < 46.5071551930507$$
$$x > 48.5068472686294 \wedge x < 50.5065647602729$$
$$x > 52.5063046452329 \wedge x < 54.5060643619126$$
$$x > 56.505841725139 \wedge x < 58.5056348594569$$
$$x > 60.5054421461245 \wedge x < 62.5052621806364$$
$$x > 64.5050937384109 \wedge x < 66.5049357468693$$
$$x > 68.5047872625577 \wedge x < 70.5046474522816$$
$$x > 72.5045155774535 \wedge x < 74.5043909810345$$
$$x > 76.5042730765805 \wedge x < 78.5041613390078$$
$$x > 80.504055296772 \wedge x < 82.503954525213$$
$$x > 84.5038586408689 \wedge x < 86.5037672965979$$
$$x > 88.503680177377 \wedge x < 90.5035969966717$$
$$x > 92.503517493286 \wedge x < 94.5034414286219$$
$$x > 96.5033685842875 \wedge x < 98.5032987600018$$
$$x > 100.503231771756$$
Solución de la desigualdad en el gráfico