Se da la desigualdad:
(x+3)x−21<0Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
(x+3)x−21=0Resolvemos:
x1=−56.8872874671946+1.86032286071536ix2=−44.9521384954488+1.99411544075916ix3=−58.8778316729686+1.84178853387051ix4=−25.1112449913453+2.38296540126348ix5=−70.8271795602881+1.74632109061647ix6=−17.2099600294603+2.68360824963445ix7=−90.7597947338789+1.62836521591924ix8=−38.4568396359062x9=−37.0056740772593+2.11433984600809ix10=−86.7719420437028+1.64892420435825ix11=−80.7913092192972+1.68232673946798ix12=−29.0716551697201+2.27677304230924ix13=−84.7782378772484+1.65969734320076ix14=−100.731737978093+1.58198548327833ix15=−94.748197958271+1.60901098994346ix16=−60.8686957915994+1.82410112335934ix17=−96.7425917333723+1.59974823628508ix18=−92.7539304764517+1.61854526606096ix19=−102.726481081352+1.57346172649423ix20=−27.0907890733987+2.3272108918749ix21=−82.7846910846935+1.67082461336369ix22=−54.8970849606657+1.87977672254041ix23=−42.9645965196765+2.02125093078451ix24=−52.9072482013241+1.90023186656731ix25=−62.8598600250948+1.80719586629625ix26=−68.8349805874056+1.7606220710008ix27=−35.0208051943819+2.15011351456698ix28=−50.9178038200274+1.92178070237845ix29=−9.30209197655335+3.17637619455067ix30=−78.7981003801705+1.69422621080467ix31=−15.239560885993+2.78730934459328ix32=−76.8050732657004+1.70654748063028ix33=−21.1568348174579+2.51469555556647ix34=−23.1331952416106+2.44503812115936ix35=−74.8122372336441+1.71931719375897ix36=−40.9776350091113+2.05018417093157ix37=−46.9402139813358+1.96859397083766ix38=−31.0536948145328+2.23085313931056ix39=−72.8196023689177+1.73256444732902ix40=−64.8513063305415+1.79101479296641ix41=−33.0367810289505+2.1888078226796ix42=−13.2702976066491+2.90703330230029ix43=−11.2979945746145+3.04260985646899ix44=−38.9913072606523+2.08112971050121ix45=−88.7657965290299+1.63848606181836ix46=−66.8430182198927+1.77550583471965ix47=−19.1823683930737+2.59354513602772ix48=−48.9287814105527+1.94452816197746ix49=−98.7371066805192+1.59074382927615iDescartamos las soluciones complejas:
x1=−38.4568396359062Las raíces dadas
x1=−38.4568396359062son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
x0<x1Consideremos, por ejemplo, el punto
x0=x1−101=
−38.4568396359062+−101=
−38.5568396359062lo sustituimos en la expresión
(x+3)x−21<0(−38.5568396359062+3)−38.5568396359062−21<0-2.62350573786034e-61 + 4.73515095110676e-62*I < 0
Entonces
x<−38.4568396359062no se cumple
significa que la solución de la desigualdad será con:
x>−38.4568396359062 _____
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x1
(x-2)²>x(x-4)
-(x-2)>6
(-10)/((x-3)^2-5)>=0