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Resolver desigualdades/ (logx^(1/2)(cos(x))+1)/(2x^2+0.3)>0

(logx^(1/2)(cos(x))+1)/(2x^2+0.3)>0 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
  ________               
\/ log(x) *cos(x) + 1    
--------------------- > 0
         2   3           
      2*x  + --          
             10
log⁡(x)cos⁡(x)+12x2+310>0\frac{\sqrt{\log{\left(x \right)}} \cos{\left(x \right)} + 1}{2 x^{2} + \frac{3}{10}} > 0 
(sqrt(log(x))*cos(x) + 1)/(2*x^2 + 3/10) > 0
Solución detallada
Se da la desigualdad:
log⁡(x)cos⁡(x)+12x2+310>0\frac{\sqrt{\log{\left(x \right)}} \cos{\left(x \right)} + 1}{2 x^{2} + \frac{3}{10}} > 0
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
log⁡(x)cos⁡(x)+12x2+310=0\frac{\sqrt{\log{\left(x \right)}} \cos{\left(x \right)} + 1}{2 x^{2} + \frac{3}{10}} = 0
Resolvemos:
x1=71.1912792889667x_{1} = 71.1912792889667
x2=98.474533286571x_{2} = 98.474533286571
x3=39.81790749774x_{3} = 39.81790749774
x4=21.0304855439734x_{4} = 21.0304855439734
x5=16.6398016669406x_{5} = 16.6398016669406
x6=−14.5888124902477+0.226872717278656ix_{6} = -14.5888124902477 + 0.226872717278656 i
x7=92.1875094576666x_{7} = 92.1875094576666
x8=10.281291113331x_{8} = 10.281291113331
x9=−39.7038117619331+0.17233651300255ix_{9} = -39.7038117619331 + 0.17233651300255 i
x10=−96.2321309612412+0.137179335755008ix_{10} = -96.2321309612412 + 0.137179335755008 i
x11=−45.9837737712157+0.165738764495262ix_{11} = -45.9837737712157 + 0.165738764495262 i
x12=52.3629208376902x_{12} = 52.3629208376902
x13=−8.30976228954732+0.265285357278091ix_{13} = -8.30976228954732 + 0.265285357278091 i
x14=73.3238866173867x_{14} = 73.3238866173867
x15=33.5494926868552x_{15} = 33.5494926868552
x16=2.89542674062072x_{16} = 2.89542674062072
x17=41.8676121416725x_{17} = 41.8676121416725
x18=96.3054969471318x_{18} = 96.3054969471318
x19=−2.00403434136006+0.381685209669179ix_{19} = -2.00403434136006 + 0.381685209669179 i
x20=46.0893682722708x_{20} = 46.0893682722708
x21=−33.4242689303608−0.180502407081655ix_{21} = -33.4242689303608 - 0.180502407081655 i
x22=85.900110905374x_{22} = 85.900110905374
x23=67.0348489150335x_{23} = 67.0348489150335
x24=48.1617912315399x_{24} = 48.1617912315399
x25=−20.8667854490919+0.205372682871723ix_{25} = -20.8667854490919 + 0.205372682871723 i
x26=35.5707249305613x_{26} = 35.5707249305613
x27=77.4690706575254x_{27} = 77.4690706575254
x28=−27.1452347681677+0.191019151516423ix_{28} = -27.1452347681677 + 0.191019151516423 i
x29=−64.8254962012094+0.151548289135052ix_{29} = -64.8254962012094 + 0.151548289135052 i
x30=−71.1065236432573+0.148006153381578ix_{30} = -71.1065236432573 + 0.148006153381578 i
x31=−83.6690686014435+0.142043989123022ix_{31} = -83.6690686014435 + 0.142043989123022 i
x32=−89.9505434161105−0.139497269580281ix_{32} = -89.9505434161105 - 0.139497269580281 i
x33=−77.3877222898321+0.144862032629662ix_{33} = -77.3877222898321 + 0.144862032629662 i
x34=79.612267055827x_{34} = 79.612267055827
x35=−77.3877222898321−0.144862032629662ix_{35} = -77.3877222898321 - 0.144862032629662 i
x36=60.7449902944826x_{36} = 60.7449902944826
x37=90.0262672782923x_{37} = 90.0262672782923
x38=3.6362645418106x_{38} = 3.6362645418106
x39=−33.4242689303608+0.180502407081655ix_{39} = -33.4242689303608 + 0.180502407081655 i
x40=83.7474330794998x_{40} = 83.7474330794998
x41=27.2858437418209x_{41} = 27.2858437418209
x42=−52.2640794943649+0.160251249342434ix_{42} = -52.2640794943649 + 0.160251249342434 i
x43=54.4540818737093x_{43} = 54.4540818737093
x44=58.6379866203864x_{44} = 58.6379866203864
x45=−58.5446692207647+0.155585268948379ix_{45} = -58.5446692207647 + 0.155585268948379 i
x46=14.7922764129932x_{46} = 14.7922764129932
x47=−45.9837737712157−0.165738764495262ix_{47} = -45.9837737712157 - 0.165738764495262 i
x48=64.9141910839444x_{48} = 64.9141910839444
x49=8.6039855648616x_{49} = 8.6039855648616
x50=22.9616469753377x_{50} = 22.9616469753377
x51=−89.9505434161105+0.139497269580281ix_{51} = -89.9505434161105 + 0.139497269580281 i
x52=29.2696879165931x_{52} = 29.2696879165931
Descartamos las soluciones complejas:
x1=71.1912792889667x_{1} = 71.1912792889667
x2=98.474533286571x_{2} = 98.474533286571
x3=39.81790749774x_{3} = 39.81790749774
x4=21.0304855439734x_{4} = 21.0304855439734
x5=16.6398016669406x_{5} = 16.6398016669406
x6=92.1875094576666x_{6} = 92.1875094576666
x7=10.281291113331x_{7} = 10.281291113331
x8=52.3629208376902x_{8} = 52.3629208376902
x9=73.3238866173867x_{9} = 73.3238866173867
x10=33.5494926868552x_{10} = 33.5494926868552
x11=2.89542674062072x_{11} = 2.89542674062072
x12=41.8676121416725x_{12} = 41.8676121416725
x13=96.3054969471318x_{13} = 96.3054969471318
x14=46.0893682722708x_{14} = 46.0893682722708
x15=85.900110905374x_{15} = 85.900110905374
x16=67.0348489150335x_{16} = 67.0348489150335
x17=48.1617912315399x_{17} = 48.1617912315399
x18=35.5707249305613x_{18} = 35.5707249305613
x19=77.4690706575254x_{19} = 77.4690706575254
x20=79.612267055827x_{20} = 79.612267055827
x21=60.7449902944826x_{21} = 60.7449902944826
x22=90.0262672782923x_{22} = 90.0262672782923
x23=3.6362645418106x_{23} = 3.6362645418106
x24=83.7474330794998x_{24} = 83.7474330794998
x25=27.2858437418209x_{25} = 27.2858437418209
x26=54.4540818737093x_{26} = 54.4540818737093
x27=58.6379866203864x_{27} = 58.6379866203864
x28=14.7922764129932x_{28} = 14.7922764129932
x29=64.9141910839444x_{29} = 64.9141910839444
x30=8.6039855648616x_{30} = 8.6039855648616
x31=22.9616469753377x_{31} = 22.9616469753377
x32=29.2696879165931x_{32} = 29.2696879165931
Las raíces dadas
x11=2.89542674062072x_{11} = 2.89542674062072
x23=3.6362645418106x_{23} = 3.6362645418106
x30=8.6039855648616x_{30} = 8.6039855648616
x7=10.281291113331x_{7} = 10.281291113331
x28=14.7922764129932x_{28} = 14.7922764129932
x5=16.6398016669406x_{5} = 16.6398016669406
x4=21.0304855439734x_{4} = 21.0304855439734
x31=22.9616469753377x_{31} = 22.9616469753377
x25=27.2858437418209x_{25} = 27.2858437418209
x32=29.2696879165931x_{32} = 29.2696879165931
x10=33.5494926868552x_{10} = 33.5494926868552
x18=35.5707249305613x_{18} = 35.5707249305613
x3=39.81790749774x_{3} = 39.81790749774
x12=41.8676121416725x_{12} = 41.8676121416725
x14=46.0893682722708x_{14} = 46.0893682722708
x17=48.1617912315399x_{17} = 48.1617912315399
x8=52.3629208376902x_{8} = 52.3629208376902
x26=54.4540818737093x_{26} = 54.4540818737093
x27=58.6379866203864x_{27} = 58.6379866203864
x21=60.7449902944826x_{21} = 60.7449902944826
x29=64.9141910839444x_{29} = 64.9141910839444
x16=67.0348489150335x_{16} = 67.0348489150335
x1=71.1912792889667x_{1} = 71.1912792889667
x9=73.3238866173867x_{9} = 73.3238866173867
x19=77.4690706575254x_{19} = 77.4690706575254
x20=79.612267055827x_{20} = 79.612267055827
x24=83.7474330794998x_{24} = 83.7474330794998
x15=85.900110905374x_{15} = 85.900110905374
x22=90.0262672782923x_{22} = 90.0262672782923
x6=92.1875094576666x_{6} = 92.1875094576666
x13=96.3054969471318x_{13} = 96.3054969471318
x2=98.474533286571x_{2} = 98.474533286571
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
x0<x11x_{0} < x_{11}
Consideremos, por ejemplo, el punto
x0=x11−110x_{0} = x_{11} - \frac{1}{10}
=
−110+2.89542674062072- \frac{1}{10} + 2.89542674062072
=
2.795426740620722.79542674062072
lo sustituimos en la expresión
log⁡(x)cos⁡(x)+12x2+310>0\frac{\sqrt{\log{\left(x \right)}} \cos{\left(x \right)} + 1}{2 x^{2} + \frac{3}{10}} > 0
log⁡(2.79542674062072)cos⁡(2.79542674062072)+1310+2⋅2.795426740620722>0\frac{\sqrt{\log{\left(2.79542674062072 \right)}} \cos{\left(2.79542674062072 \right)} + 1}{\frac{3}{10} + 2 \cdot 2.79542674062072^{2}} > 0
0.00290341311615150 > 0

significa que una de las soluciones de nuestra ecuación será con:
x<2.89542674062072x < 2.89542674062072
 _____           _____           _____           _____           _____           _____           _____           _____           _____           _____           _____           _____           _____           _____           _____           _____           _____          
      \         /     \         /     \         /     \         /     \         /     \         /     \         /     \         /     \         /     \         /     \         /     \         /     \         /     \         /     \         /     \         /
-------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-------
       x11      x23      x30      x7      x28      x5      x4      x31      x25      x32      x10      x18      x3      x12      x14      x17      x8      x26      x27      x21      x29      x16      x1      x9      x19      x20      x24      x15      x22      x6      x13      x2

Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
x<2.89542674062072x < 2.89542674062072
x>3.6362645418106∧x<8.6039855648616x > 3.6362645418106 \wedge x < 8.6039855648616
x>10.281291113331∧x<14.7922764129932x > 10.281291113331 \wedge x < 14.7922764129932
x>16.6398016669406∧x<21.0304855439734x > 16.6398016669406 \wedge x < 21.0304855439734
x>22.9616469753377∧x<27.2858437418209x > 22.9616469753377 \wedge x < 27.2858437418209
x>29.2696879165931∧x<33.5494926868552x > 29.2696879165931 \wedge x < 33.5494926868552
x>35.5707249305613∧x<39.81790749774x > 35.5707249305613 \wedge x < 39.81790749774
x>41.8676121416725∧x<46.0893682722708x > 41.8676121416725 \wedge x < 46.0893682722708
x>48.1617912315399∧x<52.3629208376902x > 48.1617912315399 \wedge x < 52.3629208376902
x>54.4540818737093∧x<58.6379866203864x > 54.4540818737093 \wedge x < 58.6379866203864
x>60.7449902944826∧x<64.9141910839444x > 60.7449902944826 \wedge x < 64.9141910839444
x>67.0348489150335∧x<71.1912792889667x > 67.0348489150335 \wedge x < 71.1912792889667
x>73.3238866173867∧x<77.4690706575254x > 73.3238866173867 \wedge x < 77.4690706575254
x>79.612267055827∧x<83.7474330794998x > 79.612267055827 \wedge x < 83.7474330794998
x>85.900110905374∧x<90.0262672782923x > 85.900110905374 \wedge x < 90.0262672782923
x>92.1875094576666∧x<96.3054969471318x > 92.1875094576666 \wedge x < 96.3054969471318
x>98.474533286571x > 98.474533286571
Solución de la desigualdad en el gráfico
02468-6-4-210120.5-0.5
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