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(x+3)^(x-0,5)<0 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
       x - 1/2    
(x + 3)        < 0
(x+3)x12<0\left(x + 3\right)^{x - \frac{1}{2}} < 0
(x + 3)^(x - 1/2) < 0
Solución detallada
Se da la desigualdad:
(x+3)x12<0\left(x + 3\right)^{x - \frac{1}{2}} < 0
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
(x+3)x12=0\left(x + 3\right)^{x - \frac{1}{2}} = 0
Resolvemos:
x1=56.8872874671946+1.86032286071536ix_{1} = -56.8872874671946 + 1.86032286071536 i
x2=44.9521384954488+1.99411544075916ix_{2} = -44.9521384954488 + 1.99411544075916 i
x3=58.8778316729686+1.84178853387051ix_{3} = -58.8778316729686 + 1.84178853387051 i
x4=25.1112449913453+2.38296540126348ix_{4} = -25.1112449913453 + 2.38296540126348 i
x5=70.8271795602881+1.74632109061647ix_{5} = -70.8271795602881 + 1.74632109061647 i
x6=17.2099600294603+2.68360824963445ix_{6} = -17.2099600294603 + 2.68360824963445 i
x7=90.7597947338789+1.62836521591924ix_{7} = -90.7597947338789 + 1.62836521591924 i
x8=38.4568396359062x_{8} = -38.4568396359062
x9=37.0056740772593+2.11433984600809ix_{9} = -37.0056740772593 + 2.11433984600809 i
x10=86.7719420437028+1.64892420435825ix_{10} = -86.7719420437028 + 1.64892420435825 i
x11=80.7913092192972+1.68232673946798ix_{11} = -80.7913092192972 + 1.68232673946798 i
x12=29.0716551697201+2.27677304230924ix_{12} = -29.0716551697201 + 2.27677304230924 i
x13=84.7782378772484+1.65969734320076ix_{13} = -84.7782378772484 + 1.65969734320076 i
x14=100.731737978093+1.58198548327833ix_{14} = -100.731737978093 + 1.58198548327833 i
x15=94.748197958271+1.60901098994346ix_{15} = -94.748197958271 + 1.60901098994346 i
x16=60.8686957915994+1.82410112335934ix_{16} = -60.8686957915994 + 1.82410112335934 i
x17=96.7425917333723+1.59974823628508ix_{17} = -96.7425917333723 + 1.59974823628508 i
x18=92.7539304764517+1.61854526606096ix_{18} = -92.7539304764517 + 1.61854526606096 i
x19=102.726481081352+1.57346172649423ix_{19} = -102.726481081352 + 1.57346172649423 i
x20=27.0907890733987+2.3272108918749ix_{20} = -27.0907890733987 + 2.3272108918749 i
x21=82.7846910846935+1.67082461336369ix_{21} = -82.7846910846935 + 1.67082461336369 i
x22=54.8970849606657+1.87977672254041ix_{22} = -54.8970849606657 + 1.87977672254041 i
x23=42.9645965196765+2.02125093078451ix_{23} = -42.9645965196765 + 2.02125093078451 i
x24=52.9072482013241+1.90023186656731ix_{24} = -52.9072482013241 + 1.90023186656731 i
x25=62.8598600250948+1.80719586629625ix_{25} = -62.8598600250948 + 1.80719586629625 i
x26=68.8349805874056+1.7606220710008ix_{26} = -68.8349805874056 + 1.7606220710008 i
x27=35.0208051943819+2.15011351456698ix_{27} = -35.0208051943819 + 2.15011351456698 i
x28=50.9178038200274+1.92178070237845ix_{28} = -50.9178038200274 + 1.92178070237845 i
x29=9.30209197655335+3.17637619455067ix_{29} = -9.30209197655335 + 3.17637619455067 i
x30=78.7981003801705+1.69422621080467ix_{30} = -78.7981003801705 + 1.69422621080467 i
x31=15.239560885993+2.78730934459328ix_{31} = -15.239560885993 + 2.78730934459328 i
x32=76.8050732657004+1.70654748063028ix_{32} = -76.8050732657004 + 1.70654748063028 i
x33=21.1568348174579+2.51469555556647ix_{33} = -21.1568348174579 + 2.51469555556647 i
x34=23.1331952416106+2.44503812115936ix_{34} = -23.1331952416106 + 2.44503812115936 i
x35=74.8122372336441+1.71931719375897ix_{35} = -74.8122372336441 + 1.71931719375897 i
x36=40.9776350091113+2.05018417093157ix_{36} = -40.9776350091113 + 2.05018417093157 i
x37=46.9402139813358+1.96859397083766ix_{37} = -46.9402139813358 + 1.96859397083766 i
x38=31.0536948145328+2.23085313931056ix_{38} = -31.0536948145328 + 2.23085313931056 i
x39=72.8196023689177+1.73256444732902ix_{39} = -72.8196023689177 + 1.73256444732902 i
x40=64.8513063305415+1.79101479296641ix_{40} = -64.8513063305415 + 1.79101479296641 i
x41=33.0367810289505+2.1888078226796ix_{41} = -33.0367810289505 + 2.1888078226796 i
x42=13.2702976066491+2.90703330230029ix_{42} = -13.2702976066491 + 2.90703330230029 i
x43=11.2979945746145+3.04260985646899ix_{43} = -11.2979945746145 + 3.04260985646899 i
x44=38.9913072606523+2.08112971050121ix_{44} = -38.9913072606523 + 2.08112971050121 i
x45=88.7657965290299+1.63848606181836ix_{45} = -88.7657965290299 + 1.63848606181836 i
x46=66.8430182198927+1.77550583471965ix_{46} = -66.8430182198927 + 1.77550583471965 i
x47=19.1823683930737+2.59354513602772ix_{47} = -19.1823683930737 + 2.59354513602772 i
x48=48.9287814105527+1.94452816197746ix_{48} = -48.9287814105527 + 1.94452816197746 i
x49=98.7371066805192+1.59074382927615ix_{49} = -98.7371066805192 + 1.59074382927615 i
Descartamos las soluciones complejas:
x1=38.4568396359062x_{1} = -38.4568396359062
Las raíces dadas
x1=38.4568396359062x_{1} = -38.4568396359062
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
x0<x1x_{0} < x_{1}
Consideremos, por ejemplo, el punto
x0=x1110x_{0} = x_{1} - \frac{1}{10}
=
38.4568396359062+110-38.4568396359062 + - \frac{1}{10}
=
38.5568396359062-38.5568396359062
lo sustituimos en la expresión
(x+3)x12<0\left(x + 3\right)^{x - \frac{1}{2}} < 0
(38.5568396359062+3)38.556839635906212<0\left(-38.5568396359062 + 3\right)^{-38.5568396359062 - \frac{1}{2}} < 0
-2.62350573786034e-61 + 4.73515095110676e-62*I < 0

Entonces
x<38.4568396359062x < -38.4568396359062
no se cumple
significa que la solución de la desigualdad será con:
x>38.4568396359062x > -38.4568396359062
         _____  
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       x1
Solución de la desigualdad en el gráfico
501234-9-8-7-6-5-4-3-2-1-10050000000000