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^2-10x<0
-
(x-2)^2/(x-1)<0
-
-x^2+3x-2<0
-
4x-4>=9x+6
-
Expresiones idénticas
- tg^2a-4tga+ tres < cero
- tg al cuadrado a menos 4tga más 3 menos 0
- tg al cuadrado a menos 4tga más tres menos cero
- tg2a-4tga+3<0
- tg²a-4tga+3<0
- tg en el grado 2a-4tga+3<0
-
Expresiones semejantes
- tg^2a+4tga+3<0
- tg^2a-4tga-3<0
-
Expresiones con funciones
- tg
- tg2x=>1
- tg(x)>-(sqr(3))/3
- tg(-x:2)>1,7
- tg(x)>3sqrt/3
- tg(x/7-5пи/6)<-√3
tg^2a-4tga+3<0 desigualdades
Solución
Ha introducido
[src]
2 tan (a) - 4*tan(a) + 3 < 0
$$\left(\tan^{2}{\left(a \right)} - 4 \tan{\left(a \right)}\right) + 3 < 0$$
tan(a)^2 - 4*tan(a) + 3 < 0
Solución detallada
Se da la desigualdad:
$$\left(\tan^{2}{\left(a \right)} - 4 \tan{\left(a \right)}\right) + 3 < 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(\tan^{2}{\left(a \right)} - 4 \tan{\left(a \right)}\right) + 3 = 0$$
Resolvemos:
$$x_{1} = -30.1668807634997$$
$$x_{2} = -5.49778714378214$$
$$x_{3} = -55.7632696012188$$
$$x_{4} = 32.2013246992954$$
$$x_{5} = -30.6305283725005$$
$$x_{6} = 51.0508806208341$$
$$x_{7} = 63.6172512351933$$
$$x_{8} = 25.9181393921158$$
$$x_{9} = 3.92699081698724$$
$$x_{10} = 29.0597320457056$$
$$x_{11} = -8.63937979737193$$
$$x_{12} = -8.17573218837112$$
$$x_{13} = 98.174770424681$$
$$x_{14} = -99.7455667514759$$
$$x_{15} = 64.0808988441941$$
$$x_{16} = -14.9225651045515$$
$$x_{17} = -40.0553063332699$$
$$x_{18} = 35.3429173528852$$
$$x_{19} = -23.8836954563201$$
$$x_{20} = -71.4712328691678$$
$$x_{21} = -36.9137136796801$$
$$x_{22} = 44.7676953136546$$
$$x_{23} = -96.6039740978861$$
$$x_{24} = 95.0331777710912$$
$$x_{25} = 38.484510006475$$
$$x_{26} = -77.7544181763474$$
$$x_{27} = -52.621676947629$$
$$x_{28} = -1.89254688119154$$
$$x_{29} = 22.776546738526$$
$$x_{30} = -27.4889357189107$$
$$x_{31} = -74.6128255227576$$
$$x_{32} = 35.806564961886$$
$$x_{33} = 54.1924732744239$$
$$x_{34} = -21.2057504117311$$
$$x_{35} = -2.35619449019234$$
$$x_{36} = -87.1791961371168$$
$$x_{37} = -52.1580293386282$$
$$x_{38} = 69.9004365423729$$
$$x_{39} = 79.3252145031423$$
$$x_{40} = -58.9048622548086$$
$$x_{41} = 82.4668071567321$$
$$x_{42} = -45.8748440314486$$
$$x_{43} = 13.8154163867574$$
$$x_{44} = -33.7721210260903$$
$$x_{45} = -80.8960108299372$$
$$x_{46} = 42.0897502690656$$
$$x_{47} = -46.3384916404494$$
$$x_{48} = 60.4756585816035$$
$$x_{49} = 101.316363078271$$
$$x_{50} = -68.329640215578$$
$$x_{51} = -74.1491779137568$$
$$x_{52} = 85.6083998103219$$
$$x_{53} = -43.1968989868597$$
$$x_{54} = -65.1880475619882$$
$$x_{55} = 13.3517687777566$$
$$x_{56} = -62.0464549083984$$
$$x_{57} = 88.7499924639117$$
$$x_{58} = 10.2101761241668$$
$$x_{59} = 0.785398163397448$$
$$x_{60} = 73.0420291959627$$
$$x_{61} = 566.27207580956$$
$$x_{62} = -96.1403264888853$$
$$x_{63} = 57.3340659280137$$
$$x_{64} = -90.3207887907066$$
$$x_{65} = -93.4623814442964$$
$$x_{66} = 86.0720474193227$$
$$x_{67} = 66.7588438887831$$
$$x_{68} = 7.06858347057703$$
$$x_{69} = 19.6349540849362$$
$$x_{70} = -89.8571411817058$$
$$x_{71} = 20.098601693937$$
$$x_{72} = -18.0641577581413$$
$$x_{73} = 16.4933614313464$$
$$x_{74} = -24.3473430653209$$
$$x_{75} = -84.037603483527$$
$$x_{76} = 47.9092879672443$$
$$x_{77} = 57.7977135370145$$
$$x_{78} = 91.8915851175014$$
$$x_{79} = -49.4800842940392$$
$$x_{80} = -11.7809724509617$$
$$x_{81} = 76.1836218495525$$
$$x_{82} = 41.6261026600648$$
$$x_{83} = -67.8659926065772$$
$$x_{1} = -30.1668807634997$$
$$x_{2} = -5.49778714378214$$
$$x_{3} = -55.7632696012188$$
$$x_{4} = 32.2013246992954$$
$$x_{5} = -30.6305283725005$$
$$x_{6} = 51.0508806208341$$
$$x_{7} = 63.6172512351933$$
$$x_{8} = 25.9181393921158$$
$$x_{9} = 3.92699081698724$$
$$x_{10} = 29.0597320457056$$
$$x_{11} = -8.63937979737193$$
$$x_{12} = -8.17573218837112$$
$$x_{13} = 98.174770424681$$
$$x_{14} = -99.7455667514759$$
$$x_{15} = 64.0808988441941$$
$$x_{16} = -14.9225651045515$$
$$x_{17} = -40.0553063332699$$
$$x_{18} = 35.3429173528852$$
$$x_{19} = -23.8836954563201$$
$$x_{20} = -71.4712328691678$$
$$x_{21} = -36.9137136796801$$
$$x_{22} = 44.7676953136546$$
$$x_{23} = -96.6039740978861$$
$$x_{24} = 95.0331777710912$$
$$x_{25} = 38.484510006475$$
$$x_{26} = -77.7544181763474$$
$$x_{27} = -52.621676947629$$
$$x_{28} = -1.89254688119154$$
$$x_{29} = 22.776546738526$$
$$x_{30} = -27.4889357189107$$
$$x_{31} = -74.6128255227576$$
$$x_{32} = 35.806564961886$$
$$x_{33} = 54.1924732744239$$
$$x_{34} = -21.2057504117311$$
$$x_{35} = -2.35619449019234$$
$$x_{36} = -87.1791961371168$$
$$x_{37} = -52.1580293386282$$
$$x_{38} = 69.9004365423729$$
$$x_{39} = 79.3252145031423$$
$$x_{40} = -58.9048622548086$$
$$x_{41} = 82.4668071567321$$
$$x_{42} = -45.8748440314486$$
$$x_{43} = 13.8154163867574$$
$$x_{44} = -33.7721210260903$$
$$x_{45} = -80.8960108299372$$
$$x_{46} = 42.0897502690656$$
$$x_{47} = -46.3384916404494$$
$$x_{48} = 60.4756585816035$$
$$x_{49} = 101.316363078271$$
$$x_{50} = -68.329640215578$$
$$x_{51} = -74.1491779137568$$
$$x_{52} = 85.6083998103219$$
$$x_{53} = -43.1968989868597$$
$$x_{54} = -65.1880475619882$$
$$x_{55} = 13.3517687777566$$
$$x_{56} = -62.0464549083984$$
$$x_{57} = 88.7499924639117$$
$$x_{58} = 10.2101761241668$$
$$x_{59} = 0.785398163397448$$
$$x_{60} = 73.0420291959627$$
$$x_{61} = 566.27207580956$$
$$x_{62} = -96.1403264888853$$
$$x_{63} = 57.3340659280137$$
$$x_{64} = -90.3207887907066$$
$$x_{65} = -93.4623814442964$$
$$x_{66} = 86.0720474193227$$
$$x_{67} = 66.7588438887831$$
$$x_{68} = 7.06858347057703$$
$$x_{69} = 19.6349540849362$$
$$x_{70} = -89.8571411817058$$
$$x_{71} = 20.098601693937$$
$$x_{72} = -18.0641577581413$$
$$x_{73} = 16.4933614313464$$
$$x_{74} = -24.3473430653209$$
$$x_{75} = -84.037603483527$$
$$x_{76} = 47.9092879672443$$
$$x_{77} = 57.7977135370145$$
$$x_{78} = 91.8915851175014$$
$$x_{79} = -49.4800842940392$$
$$x_{80} = -11.7809724509617$$
$$x_{81} = 76.1836218495525$$
$$x_{82} = 41.6261026600648$$
$$x_{83} = -67.8659926065772$$
Las raíces dadas
$$x_{14} = -99.7455667514759$$
$$x_{23} = -96.6039740978861$$
$$x_{62} = -96.1403264888853$$
$$x_{65} = -93.4623814442964$$
$$x_{64} = -90.3207887907066$$
$$x_{70} = -89.8571411817058$$
$$x_{36} = -87.1791961371168$$
$$x_{75} = -84.037603483527$$
$$x_{45} = -80.8960108299372$$
$$x_{26} = -77.7544181763474$$
$$x_{31} = -74.6128255227576$$
$$x_{51} = -74.1491779137568$$
$$x_{20} = -71.4712328691678$$
$$x_{50} = -68.329640215578$$
$$x_{83} = -67.8659926065772$$
$$x_{54} = -65.1880475619882$$
$$x_{56} = -62.0464549083984$$
$$x_{40} = -58.9048622548086$$
$$x_{3} = -55.7632696012188$$
$$x_{27} = -52.621676947629$$
$$x_{37} = -52.1580293386282$$
$$x_{79} = -49.4800842940392$$
$$x_{47} = -46.3384916404494$$
$$x_{42} = -45.8748440314486$$
$$x_{53} = -43.1968989868597$$
$$x_{17} = -40.0553063332699$$
$$x_{21} = -36.9137136796801$$
$$x_{44} = -33.7721210260903$$
$$x_{5} = -30.6305283725005$$
$$x_{1} = -30.1668807634997$$
$$x_{30} = -27.4889357189107$$
$$x_{74} = -24.3473430653209$$
$$x_{19} = -23.8836954563201$$
$$x_{34} = -21.2057504117311$$
$$x_{72} = -18.0641577581413$$
$$x_{16} = -14.9225651045515$$
$$x_{80} = -11.7809724509617$$
$$x_{11} = -8.63937979737193$$
$$x_{12} = -8.17573218837112$$
$$x_{2} = -5.49778714378214$$
$$x_{35} = -2.35619449019234$$
$$x_{28} = -1.89254688119154$$
$$x_{59} = 0.785398163397448$$
$$x_{9} = 3.92699081698724$$
$$x_{68} = 7.06858347057703$$
$$x_{58} = 10.2101761241668$$
$$x_{55} = 13.3517687777566$$
$$x_{43} = 13.8154163867574$$
$$x_{73} = 16.4933614313464$$
$$x_{69} = 19.6349540849362$$
$$x_{71} = 20.098601693937$$
$$x_{29} = 22.776546738526$$
$$x_{8} = 25.9181393921158$$
$$x_{10} = 29.0597320457056$$
$$x_{4} = 32.2013246992954$$
$$x_{18} = 35.3429173528852$$
$$x_{32} = 35.806564961886$$
$$x_{25} = 38.484510006475$$
$$x_{82} = 41.6261026600648$$
$$x_{46} = 42.0897502690656$$
$$x_{22} = 44.7676953136546$$
$$x_{76} = 47.9092879672443$$
$$x_{6} = 51.0508806208341$$
$$x_{33} = 54.1924732744239$$
$$x_{63} = 57.3340659280137$$
$$x_{77} = 57.7977135370145$$
$$x_{48} = 60.4756585816035$$
$$x_{7} = 63.6172512351933$$
$$x_{15} = 64.0808988441941$$
$$x_{67} = 66.7588438887831$$
$$x_{38} = 69.9004365423729$$
$$x_{60} = 73.0420291959627$$
$$x_{81} = 76.1836218495525$$
$$x_{39} = 79.3252145031423$$
$$x_{41} = 82.4668071567321$$
$$x_{52} = 85.6083998103219$$
$$x_{66} = 86.0720474193227$$
$$x_{57} = 88.7499924639117$$
$$x_{78} = 91.8915851175014$$
$$x_{24} = 95.0331777710912$$
$$x_{13} = 98.174770424681$$
$$x_{49} = 101.316363078271$$
$$x_{61} = 566.27207580956$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{14}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{14} - \frac{1}{10}$$
=
$$-99.7455667514759 + - \frac{1}{10}$$
=
$$-99.8455667514759$$
lo sustituimos en la expresión
$$\left(\tan^{2}{\left(a \right)} - 4 \tan{\left(a \right)}\right) + 3 < 0$$
$$\left(\tan^{2}{\left(a \right)} - 4 \tan{\left(a \right)}\right) + 3 < 0$$
Entonces
$$x < -99.7455667514759$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -99.7455667514759 \wedge x < -96.6039740978861$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -99.7455667514759 \wedge x < -96.6039740978861$$
$$x > -96.1403264888853 \wedge x < -93.4623814442964$$
$$x > -90.3207887907066 \wedge x < -89.8571411817058$$
$$x > -87.1791961371168 \wedge x < -84.037603483527$$
$$x > -80.8960108299372 \wedge x < -77.7544181763474$$
$$x > -74.6128255227576 \wedge x < -74.1491779137568$$
$$x > -71.4712328691678 \wedge x < -68.329640215578$$
$$x > -67.8659926065772 \wedge x < -65.1880475619882$$
$$x > -62.0464549083984 \wedge x < -58.9048622548086$$
$$x > -55.7632696012188 \wedge x < -52.621676947629$$
$$x > -52.1580293386282 \wedge x < -49.4800842940392$$
$$x > -46.3384916404494 \wedge x < -45.8748440314486$$
$$x > -43.1968989868597 \wedge x < -40.0553063332699$$
$$x > -36.9137136796801 \wedge x < -33.7721210260903$$
$$x > -30.6305283725005 \wedge x < -30.1668807634997$$
$$x > -27.4889357189107 \wedge x < -24.3473430653209$$
$$x > -23.8836954563201 \wedge x < -21.2057504117311$$
$$x > -18.0641577581413 \wedge x < -14.9225651045515$$
$$x > -11.7809724509617 \wedge x < -8.63937979737193$$
$$x > -8.17573218837112 \wedge x < -5.49778714378214$$
$$x > -2.35619449019234 \wedge x < -1.89254688119154$$
$$x > 0.785398163397448 \wedge x < 3.92699081698724$$
$$x > 7.06858347057703 \wedge x < 10.2101761241668$$
$$x > 13.3517687777566 \wedge x < 13.8154163867574$$
$$x > 16.4933614313464 \wedge x < 19.6349540849362$$
$$x > 20.098601693937 \wedge x < 22.776546738526$$
$$x > 25.9181393921158 \wedge x < 29.0597320457056$$
$$x > 32.2013246992954 \wedge x < 35.3429173528852$$
$$x > 35.806564961886 \wedge x < 38.484510006475$$
$$x > 41.6261026600648 \wedge x < 42.0897502690656$$
$$x > 44.7676953136546 \wedge x < 47.9092879672443$$
$$x > 51.0508806208341 \wedge x < 54.1924732744239$$
$$x > 57.3340659280137 \wedge x < 57.7977135370145$$
$$x > 60.4756585816035 \wedge x < 63.6172512351933$$
$$x > 64.0808988441941 \wedge x < 66.7588438887831$$
$$x > 69.9004365423729 \wedge x < 73.0420291959627$$
$$x > 76.1836218495525 \wedge x < 79.3252145031423$$
$$x > 82.4668071567321 \wedge x < 85.6083998103219$$
$$x > 86.0720474193227 \wedge x < 88.7499924639117$$
$$x > 91.8915851175014 \wedge x < 95.0331777710912$$
$$x > 98.174770424681 \wedge x < 101.316363078271$$
$$x > 566.27207580956$$
$$\left(\tan^{2}{\left(a \right)} - 4 \tan{\left(a \right)}\right) + 3 < 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(\tan^{2}{\left(a \right)} - 4 \tan{\left(a \right)}\right) + 3 = 0$$
Resolvemos:
$$x_{1} = -30.1668807634997$$
$$x_{2} = -5.49778714378214$$
$$x_{3} = -55.7632696012188$$
$$x_{4} = 32.2013246992954$$
$$x_{5} = -30.6305283725005$$
$$x_{6} = 51.0508806208341$$
$$x_{7} = 63.6172512351933$$
$$x_{8} = 25.9181393921158$$
$$x_{9} = 3.92699081698724$$
$$x_{10} = 29.0597320457056$$
$$x_{11} = -8.63937979737193$$
$$x_{12} = -8.17573218837112$$
$$x_{13} = 98.174770424681$$
$$x_{14} = -99.7455667514759$$
$$x_{15} = 64.0808988441941$$
$$x_{16} = -14.9225651045515$$
$$x_{17} = -40.0553063332699$$
$$x_{18} = 35.3429173528852$$
$$x_{19} = -23.8836954563201$$
$$x_{20} = -71.4712328691678$$
$$x_{21} = -36.9137136796801$$
$$x_{22} = 44.7676953136546$$
$$x_{23} = -96.6039740978861$$
$$x_{24} = 95.0331777710912$$
$$x_{25} = 38.484510006475$$
$$x_{26} = -77.7544181763474$$
$$x_{27} = -52.621676947629$$
$$x_{28} = -1.89254688119154$$
$$x_{29} = 22.776546738526$$
$$x_{30} = -27.4889357189107$$
$$x_{31} = -74.6128255227576$$
$$x_{32} = 35.806564961886$$
$$x_{33} = 54.1924732744239$$
$$x_{34} = -21.2057504117311$$
$$x_{35} = -2.35619449019234$$
$$x_{36} = -87.1791961371168$$
$$x_{37} = -52.1580293386282$$
$$x_{38} = 69.9004365423729$$
$$x_{39} = 79.3252145031423$$
$$x_{40} = -58.9048622548086$$
$$x_{41} = 82.4668071567321$$
$$x_{42} = -45.8748440314486$$
$$x_{43} = 13.8154163867574$$
$$x_{44} = -33.7721210260903$$
$$x_{45} = -80.8960108299372$$
$$x_{46} = 42.0897502690656$$
$$x_{47} = -46.3384916404494$$
$$x_{48} = 60.4756585816035$$
$$x_{49} = 101.316363078271$$
$$x_{50} = -68.329640215578$$
$$x_{51} = -74.1491779137568$$
$$x_{52} = 85.6083998103219$$
$$x_{53} = -43.1968989868597$$
$$x_{54} = -65.1880475619882$$
$$x_{55} = 13.3517687777566$$
$$x_{56} = -62.0464549083984$$
$$x_{57} = 88.7499924639117$$
$$x_{58} = 10.2101761241668$$
$$x_{59} = 0.785398163397448$$
$$x_{60} = 73.0420291959627$$
$$x_{61} = 566.27207580956$$
$$x_{62} = -96.1403264888853$$
$$x_{63} = 57.3340659280137$$
$$x_{64} = -90.3207887907066$$
$$x_{65} = -93.4623814442964$$
$$x_{66} = 86.0720474193227$$
$$x_{67} = 66.7588438887831$$
$$x_{68} = 7.06858347057703$$
$$x_{69} = 19.6349540849362$$
$$x_{70} = -89.8571411817058$$
$$x_{71} = 20.098601693937$$
$$x_{72} = -18.0641577581413$$
$$x_{73} = 16.4933614313464$$
$$x_{74} = -24.3473430653209$$
$$x_{75} = -84.037603483527$$
$$x_{76} = 47.9092879672443$$
$$x_{77} = 57.7977135370145$$
$$x_{78} = 91.8915851175014$$
$$x_{79} = -49.4800842940392$$
$$x_{80} = -11.7809724509617$$
$$x_{81} = 76.1836218495525$$
$$x_{82} = 41.6261026600648$$
$$x_{83} = -67.8659926065772$$
$$x_{1} = -30.1668807634997$$
$$x_{2} = -5.49778714378214$$
$$x_{3} = -55.7632696012188$$
$$x_{4} = 32.2013246992954$$
$$x_{5} = -30.6305283725005$$
$$x_{6} = 51.0508806208341$$
$$x_{7} = 63.6172512351933$$
$$x_{8} = 25.9181393921158$$
$$x_{9} = 3.92699081698724$$
$$x_{10} = 29.0597320457056$$
$$x_{11} = -8.63937979737193$$
$$x_{12} = -8.17573218837112$$
$$x_{13} = 98.174770424681$$
$$x_{14} = -99.7455667514759$$
$$x_{15} = 64.0808988441941$$
$$x_{16} = -14.9225651045515$$
$$x_{17} = -40.0553063332699$$
$$x_{18} = 35.3429173528852$$
$$x_{19} = -23.8836954563201$$
$$x_{20} = -71.4712328691678$$
$$x_{21} = -36.9137136796801$$
$$x_{22} = 44.7676953136546$$
$$x_{23} = -96.6039740978861$$
$$x_{24} = 95.0331777710912$$
$$x_{25} = 38.484510006475$$
$$x_{26} = -77.7544181763474$$
$$x_{27} = -52.621676947629$$
$$x_{28} = -1.89254688119154$$
$$x_{29} = 22.776546738526$$
$$x_{30} = -27.4889357189107$$
$$x_{31} = -74.6128255227576$$
$$x_{32} = 35.806564961886$$
$$x_{33} = 54.1924732744239$$
$$x_{34} = -21.2057504117311$$
$$x_{35} = -2.35619449019234$$
$$x_{36} = -87.1791961371168$$
$$x_{37} = -52.1580293386282$$
$$x_{38} = 69.9004365423729$$
$$x_{39} = 79.3252145031423$$
$$x_{40} = -58.9048622548086$$
$$x_{41} = 82.4668071567321$$
$$x_{42} = -45.8748440314486$$
$$x_{43} = 13.8154163867574$$
$$x_{44} = -33.7721210260903$$
$$x_{45} = -80.8960108299372$$
$$x_{46} = 42.0897502690656$$
$$x_{47} = -46.3384916404494$$
$$x_{48} = 60.4756585816035$$
$$x_{49} = 101.316363078271$$
$$x_{50} = -68.329640215578$$
$$x_{51} = -74.1491779137568$$
$$x_{52} = 85.6083998103219$$
$$x_{53} = -43.1968989868597$$
$$x_{54} = -65.1880475619882$$
$$x_{55} = 13.3517687777566$$
$$x_{56} = -62.0464549083984$$
$$x_{57} = 88.7499924639117$$
$$x_{58} = 10.2101761241668$$
$$x_{59} = 0.785398163397448$$
$$x_{60} = 73.0420291959627$$
$$x_{61} = 566.27207580956$$
$$x_{62} = -96.1403264888853$$
$$x_{63} = 57.3340659280137$$
$$x_{64} = -90.3207887907066$$
$$x_{65} = -93.4623814442964$$
$$x_{66} = 86.0720474193227$$
$$x_{67} = 66.7588438887831$$
$$x_{68} = 7.06858347057703$$
$$x_{69} = 19.6349540849362$$
$$x_{70} = -89.8571411817058$$
$$x_{71} = 20.098601693937$$
$$x_{72} = -18.0641577581413$$
$$x_{73} = 16.4933614313464$$
$$x_{74} = -24.3473430653209$$
$$x_{75} = -84.037603483527$$
$$x_{76} = 47.9092879672443$$
$$x_{77} = 57.7977135370145$$
$$x_{78} = 91.8915851175014$$
$$x_{79} = -49.4800842940392$$
$$x_{80} = -11.7809724509617$$
$$x_{81} = 76.1836218495525$$
$$x_{82} = 41.6261026600648$$
$$x_{83} = -67.8659926065772$$
Las raíces dadas
$$x_{14} = -99.7455667514759$$
$$x_{23} = -96.6039740978861$$
$$x_{62} = -96.1403264888853$$
$$x_{65} = -93.4623814442964$$
$$x_{64} = -90.3207887907066$$
$$x_{70} = -89.8571411817058$$
$$x_{36} = -87.1791961371168$$
$$x_{75} = -84.037603483527$$
$$x_{45} = -80.8960108299372$$
$$x_{26} = -77.7544181763474$$
$$x_{31} = -74.6128255227576$$
$$x_{51} = -74.1491779137568$$
$$x_{20} = -71.4712328691678$$
$$x_{50} = -68.329640215578$$
$$x_{83} = -67.8659926065772$$
$$x_{54} = -65.1880475619882$$
$$x_{56} = -62.0464549083984$$
$$x_{40} = -58.9048622548086$$
$$x_{3} = -55.7632696012188$$
$$x_{27} = -52.621676947629$$
$$x_{37} = -52.1580293386282$$
$$x_{79} = -49.4800842940392$$
$$x_{47} = -46.3384916404494$$
$$x_{42} = -45.8748440314486$$
$$x_{53} = -43.1968989868597$$
$$x_{17} = -40.0553063332699$$
$$x_{21} = -36.9137136796801$$
$$x_{44} = -33.7721210260903$$
$$x_{5} = -30.6305283725005$$
$$x_{1} = -30.1668807634997$$
$$x_{30} = -27.4889357189107$$
$$x_{74} = -24.3473430653209$$
$$x_{19} = -23.8836954563201$$
$$x_{34} = -21.2057504117311$$
$$x_{72} = -18.0641577581413$$
$$x_{16} = -14.9225651045515$$
$$x_{80} = -11.7809724509617$$
$$x_{11} = -8.63937979737193$$
$$x_{12} = -8.17573218837112$$
$$x_{2} = -5.49778714378214$$
$$x_{35} = -2.35619449019234$$
$$x_{28} = -1.89254688119154$$
$$x_{59} = 0.785398163397448$$
$$x_{9} = 3.92699081698724$$
$$x_{68} = 7.06858347057703$$
$$x_{58} = 10.2101761241668$$
$$x_{55} = 13.3517687777566$$
$$x_{43} = 13.8154163867574$$
$$x_{73} = 16.4933614313464$$
$$x_{69} = 19.6349540849362$$
$$x_{71} = 20.098601693937$$
$$x_{29} = 22.776546738526$$
$$x_{8} = 25.9181393921158$$
$$x_{10} = 29.0597320457056$$
$$x_{4} = 32.2013246992954$$
$$x_{18} = 35.3429173528852$$
$$x_{32} = 35.806564961886$$
$$x_{25} = 38.484510006475$$
$$x_{82} = 41.6261026600648$$
$$x_{46} = 42.0897502690656$$
$$x_{22} = 44.7676953136546$$
$$x_{76} = 47.9092879672443$$
$$x_{6} = 51.0508806208341$$
$$x_{33} = 54.1924732744239$$
$$x_{63} = 57.3340659280137$$
$$x_{77} = 57.7977135370145$$
$$x_{48} = 60.4756585816035$$
$$x_{7} = 63.6172512351933$$
$$x_{15} = 64.0808988441941$$
$$x_{67} = 66.7588438887831$$
$$x_{38} = 69.9004365423729$$
$$x_{60} = 73.0420291959627$$
$$x_{81} = 76.1836218495525$$
$$x_{39} = 79.3252145031423$$
$$x_{41} = 82.4668071567321$$
$$x_{52} = 85.6083998103219$$
$$x_{66} = 86.0720474193227$$
$$x_{57} = 88.7499924639117$$
$$x_{78} = 91.8915851175014$$
$$x_{24} = 95.0331777710912$$
$$x_{13} = 98.174770424681$$
$$x_{49} = 101.316363078271$$
$$x_{61} = 566.27207580956$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{14}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{14} - \frac{1}{10}$$
=
$$-99.7455667514759 + - \frac{1}{10}$$
=
$$-99.8455667514759$$
lo sustituimos en la expresión
$$\left(\tan^{2}{\left(a \right)} - 4 \tan{\left(a \right)}\right) + 3 < 0$$
$$\left(\tan^{2}{\left(a \right)} - 4 \tan{\left(a \right)}\right) + 3 < 0$$
2
3 + tan (a) - 4*tan(a) < 0
Entonces
$$x < -99.7455667514759$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -99.7455667514759 \wedge x < -96.6039740978861$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------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-------
x14 x23 x62 x65 x64 x70 x36 x75 x45 x26 x31 x51 x20 x50 x83 x54 x56 x40 x3 x27 x37 x79 x47 x42 x53 x17 x21 x44 x5 x1 x30 x74 x19 x34 x72 x16 x80 x11 x12 x2 x35 x28 x59 x9 x68 x58 x55 x43 x73 x69 x71 x29 x8 x10 x4 x18 x32 x25 x82 x46 x22 x76 x6 x33 x63 x77 x48 x7 x15 x67 x38 x60 x81 x39 x41 x52 x66 x57 x78 x24 x13 x49 x61Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -99.7455667514759 \wedge x < -96.6039740978861$$
$$x > -96.1403264888853 \wedge x < -93.4623814442964$$
$$x > -90.3207887907066 \wedge x < -89.8571411817058$$
$$x > -87.1791961371168 \wedge x < -84.037603483527$$
$$x > -80.8960108299372 \wedge x < -77.7544181763474$$
$$x > -74.6128255227576 \wedge x < -74.1491779137568$$
$$x > -71.4712328691678 \wedge x < -68.329640215578$$
$$x > -67.8659926065772 \wedge x < -65.1880475619882$$
$$x > -62.0464549083984 \wedge x < -58.9048622548086$$
$$x > -55.7632696012188 \wedge x < -52.621676947629$$
$$x > -52.1580293386282 \wedge x < -49.4800842940392$$
$$x > -46.3384916404494 \wedge x < -45.8748440314486$$
$$x > -43.1968989868597 \wedge x < -40.0553063332699$$
$$x > -36.9137136796801 \wedge x < -33.7721210260903$$
$$x > -30.6305283725005 \wedge x < -30.1668807634997$$
$$x > -27.4889357189107 \wedge x < -24.3473430653209$$
$$x > -23.8836954563201 \wedge x < -21.2057504117311$$
$$x > -18.0641577581413 \wedge x < -14.9225651045515$$
$$x > -11.7809724509617 \wedge x < -8.63937979737193$$
$$x > -8.17573218837112 \wedge x < -5.49778714378214$$
$$x > -2.35619449019234 \wedge x < -1.89254688119154$$
$$x > 0.785398163397448 \wedge x < 3.92699081698724$$
$$x > 7.06858347057703 \wedge x < 10.2101761241668$$
$$x > 13.3517687777566 \wedge x < 13.8154163867574$$
$$x > 16.4933614313464 \wedge x < 19.6349540849362$$
$$x > 20.098601693937 \wedge x < 22.776546738526$$
$$x > 25.9181393921158 \wedge x < 29.0597320457056$$
$$x > 32.2013246992954 \wedge x < 35.3429173528852$$
$$x > 35.806564961886 \wedge x < 38.484510006475$$
$$x > 41.6261026600648 \wedge x < 42.0897502690656$$
$$x > 44.7676953136546 \wedge x < 47.9092879672443$$
$$x > 51.0508806208341 \wedge x < 54.1924732744239$$
$$x > 57.3340659280137 \wedge x < 57.7977135370145$$
$$x > 60.4756585816035 \wedge x < 63.6172512351933$$
$$x > 64.0808988441941 \wedge x < 66.7588438887831$$
$$x > 69.9004365423729 \wedge x < 73.0420291959627$$
$$x > 76.1836218495525 \wedge x < 79.3252145031423$$
$$x > 82.4668071567321 \wedge x < 85.6083998103219$$
$$x > 86.0720474193227 \wedge x < 88.7499924639117$$
$$x > 91.8915851175014 \wedge x < 95.0331777710912$$
$$x > 98.174770424681 \wedge x < 101.316363078271$$
$$x > 566.27207580956$$
Respuesta rápida
[src]
/pi \ And|-- < a, a < atan(3)| \4 /
$$\frac{\pi}{4} < a \wedge a < \operatorname{atan}{\left(3 \right)}$$
(a < atan(3))∧(pi/4 < a)
Respuesta rápida 2
[src]
pi (--, atan(3)) 4
$$x\ in\ \left(\frac{\pi}{4}, \operatorname{atan}{\left(3 \right)}\right)$$
x in Interval.open(pi/4, atan(3))